Donald J Herzog Popular Books
Donald J Herzog Biography & Facts
In mathematics, the Herzog–Schönheim conjecture is a combinatorial problem in the area of group theory, posed by Marcel Herzog and Jochanan Schönheim in 1974.Let G{\displaystyle G} be a group, and let A={a1G1, …, akGk}{\displaystyle A=\{a_{1}G_{1},\ \ldots ,\ a_{k}G_{k}\}}be a finite system of left cosets of subgroups G1,…,Gk{\displaystyle G_{1},\ldots ,G_{k}} of G{\displaystyle G}. Herzog and Schönheim conjectured that if A{\displaystyle A} forms a partition of G{\displaystyle G} with k>1{\displaystyle k>1}, then the (finite) indices [G:G1],…,[G:Gk]{\displaystyle [G:G_{1}],\ldots ,[G:G_{k}]} cannot be distinct. In contrast, if repeated indices are allowed, then partitioning a group into cosets is easy: if H{\displaystyle H} is any subgroup of G{\displaystyle G} with index k=[G:H]<∞{\displaystyle k=[G:H]<\infty } then G{\displaystyle G} can be partitioned into k{\displaystyle k} left cosets of H{\displaystyle H}. Subnormal subgroups In 2004, Zhi-Wei Sun proved an extended version of the Herzog–Schönheim conjecture in the case where G1,…,Gk{\displaystyle G_{1},\ldots ,G_{k}} are subnormal in G{\displaystyle G}. A basic lemma in Sun's proof states that if G1,…,Gk{\displaystyle G_{1},\ldots ,G_{k}} are subnormal and of finite index in G{\displaystyle G}, then [G:⋂i=1kGi] | ∏i=1k[G:Gi]{\displaystyle {\bigg [}G:\bigcap _{i=1}^{k}G_{i}{\bigg ]}\ {\bigg |}\ \prod _{i=1}^{k}[G:G_{i}]}and hence P([G:⋂i=1kGi] )=⋃i=1kP([G:Gi]),{\displaystyle P{\bigg (}{\bigg [}G:\bigcap _{i=1}^{k}G_{i}{\bigg ]}\ {\bigg )}=\bigcup _{i=1}^{k}P([G:G_{i}]),}where P(n){\displaystyle P(n)} denotes the set of prime divisors of n{\displaystyle n}. Mirsky–Newman theorem When G{\displaystyle G} is the additive group Z{\displaystyle \mathbb {Z} } of integers, the cosets of G{\displaystyle G} are the arithmetic progressions. In this case, the Herzog–Schönheim conjecture states that every covering system, a family of arithmetic progressions that together cover all the integers, must either cover some integers more than once or include at least one pair of progressions that have the same difference as each other. This result was conjectured in 1950 by Paul Erdős and proved soon thereafter by Leon Mirsky and Donald J. Newman. However, Mirsky and Newman never published their proof. The same proof was also found independently by Harold Davenport and Richard Rado.In 1970, a geometric coloring problem equivalent to the Mirsky–Newman theorem was given in the Soviet mathematical olympiad: suppose that the vertices of a regular polygon are colored in such a way that every color class itself forms the vertices of a regular polygon. Then, there exist two color classes that form congruent polygons. References. Discover the Donald J Herzog popular books. Find the top 100 most popular Donald J Herzog books.
Best Seller Donald J Herzog Books of 2024
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Never Enough
Lexy TimmsBe good enough never is... Anthony Accardi is a man on a mission: make his father's watch company a success while bringing in millions of dollars. To do that, he needs an assi...
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The Cupcake Cottage
Jean OramNHL player Maverick Blades could fall in love with anyone... But he had to fall for a woman who falls under the Bro Code as untouchablehis best friend’s beautiful ex, DaisyMae Ray....
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Dracula
Bram StokerAn Apple Books Classic edition. Few characters have seized readers’ imaginations quite like Count Dracula of Transylvania, the hero of Bram Stoker’s classic. The 1897 novel put vam...
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Whiskey Girl
Melissa BelleThey'll do anything for each other…except commit. Logan Wild isn’t just the hottest broncriding cowboy in Texas. He’s also my best friendwith benefits. And that’s all we’ll ev...
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The Odyssey
HomerAn Apple Books Classic edition. Homer’s eighthcentury epic poem is a companion to The Iliad . It tells the story of Odysseus, who journeys by ship for 10 years after the Trojan War...
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Alpha
Sybil BartelBillionaire. Mercenary. Navy SEAL. The Teams trained me to be a killer. War taught me to be ruthless. Then an illfated mission proved I was human. Combat wounded, cut loose by the ...
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Nothing to Hide
Scarlett FinnPrize of a lifetime: travel the world with a celebrity billionaire. Come to LA with us, Roxie… It will be so much fun! We have tickets for a latenight talk show! What could possibl...
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Silenced Girls
Roger Stelljes“ Wow wow wow!  Grips you in a choke hold and  does not let go … Oozes suspense and  bonechilling twists and turns .  Astonishing … One of those...
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The Wonderful Wizard of Oz
L. Frank BaumAn Apple Books Classic edition. You’ve seen the iconic 1939 movie, but do you know about the talking field mice, the Winkies, and the Witch of the North that appear in the original...
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Teased by Fire
Molly O'HareFrom USA Today bestselling author Molly O’Hare comes an enemiestolovers, older brother’s best friend, romantic comedy with a curvy, antisocial, supernaturalobsessed, allyearround h...
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The Seduction Series Boxset
Roxy Sloane“Sensual, thrilling and wild!”   Discover the bestselling series in one collection: THE SEDUCTION, THE BARGAIN, and THE INVITATION. Perfect for fans of Ana Huang, Sierra S...
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Escape, A New Life
David J AntocciTo save herself, she had to lose everything. Trapped in a tropical paradise with no memory of how she got there, Abby is thrust into a fight for her life. Hunted by a madman, and c...
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A Bookshop to Die For
M.P. BlackDitching her fiancé at the altar, Alice Hartford bolts to her childhood hometown to reconnect with the last, happy remnant of her past: her mom's old bookstore. But the bookst...
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Think and Grow Rich
Greg Habstritt & Napoleon HillThink and Grow Rich is one of the most popular success book of alltime, having sold more than 60 million copies since it was first published more than 70...
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Awaken Me
Jenna JacobHe was more than a ghost haunting my dreams…he was real. By day, I’m Julianna Garrett …a prim, proper accountant. By night, I’m tormented by dreams of an alpha, ambereyed Adonis wh...
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Eternal
W.J. MayShe will fight for what is hers. When the king is murdered, Katerina, his only daughter, must flee for her life. She finds herself on a strange and dangerous path. Alone for the fi...
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Pride and Prejudice
Jane AustenAn Apple Books Classic edition. Jane Austen’s beloved classic opens with this witty and very memorable line: “It is a truth universally acknowledged, that a single man in possessio...
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Man In The Water
Jon HillAn attempted murder. A missing spouse. And an international conspiracy that could change the world. Jack Green has always been skeptical of socalled facts. Though he's forced ...
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His Girl Next Door
Khardine GrayFrom USA Today Bestselling author Khardine Gray comes a sizzling hot single dad romance you won't want to miss. No strings attached fun with the ubergorgeous single d...
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Always Yours
Claire RayeSome things are just meant to be... Ellen Somerville and Will McIntyre met by accident and under unusual circumstances. Getting sprayed by a skunk in a parking lot wouldn’t normall...
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Finding Cinderella
Colleen Hoover#1 New York Times bestselling author of It Starts with Us and It Ends With Us writes a free novella about the search for happily ever after. A chance encounter in the dark leads ei...
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You Are Kind
Michael GordonA little kindness goes a long way. How can you help encourage your kids to be kind from a young age? Teach kindness to preschoolers Acts of kindness can be fun, easy, and make a ...
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All Fired Up
Kathryn ShayCaptain Jarek Zenko, a war veteran and firefighter, meets Lacey Roth at a bar one night. They don’t share their real identities, even when they retreat to a hotel. When they meet t...
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Dark Psychology and Manipulation
Margaret MorrisonTHE MENTAL MANIPULATOR WILL NO LONGER KEEP SECRETS FROM YOU! Are you fed up with the wool being pulled over your eyes?Are you prepared to stand up to those who believe they can man...
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Masters of Restraint
Ines JohnsonMy new boss is good at giving orders. But his latest demand is NSFW. Especially when his two business partners want in on our deal. My new boss My boss’s boss Their investor &#...
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Get Lucky
Lila MonroeFall for the hot and hilarious romcom spin on 'The Hangover', perfect for fans of Tessa Bailey, Ali Hazelwood, and Emily Henry! What happens when you wake up in a hotel s...
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Salvation
Meghan O'FlynnIf you like mouthy detectives, serial killers, and suspenseful mysteries that don't quit, this chilling and actionpacked hardboiled detective series has you covered! Try this ...
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Wuthering Heights
Emily BrontëAn Apple Books Classic edition. If you’ve only ever seen Wuthering Heights on screen, you may have an image of Catherine and Heathcliff as the ultimate starcrossed lovers. But that...
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Coffee Girl
Sophie SinclairMackenzie "Kiki" Forbes finds herself in a pickle. Either become her snarky sister's nanny, or move halfway across the country to work as assistanttothestylist of a ...
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Holy Bible
The Church of Jesus Christ of Latter-day SaintsThe 2013 edition of the Holy Bible contains all of the study aids contained in the 1979 edition and includes revisions to the study aids, several new photos, updated maps, and adju...
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Assisting the Bosshole
Kristin MacQueenNo hot water? Check Missed the train? Check Broke my heel? Check Dropped my coffee? Check My first day of my new job can’t possibly go worse, right? Wrong. When I meet Parker Scott...
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Meditations
Emperor of Rome Marcus AureliusMeditations is a series of personal writings by Marcus Aurelius, Roman Emperor 161–180 CE, setting forth his ideas on Stoic philosophy.
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Becoming Lady Dalton
Carrie LomaxA dance of desire and deceit... In the glittering world of London's ton, Mrs. Viola Cartwright revels in her newfound freedom as a lady of leisureuntil a series of jewel theft...
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His Own Heaven
Jennie KewWinner of the 2021 Passionate Plume Award for BDSM Romance Finalist in the 2021 Stiletto Contest for Contemporary Romance He taught her to trust, she taught him to love. Lucy Bar...
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The Honeymoon Homicide
J. R. Mathis & Susan MathisEnjoy this SmallTown Murder Mystery Featuring A Unique Sleuthing Couple I'm Father Tom Greer, a Catholic Priest in a smalltown parish who never expected this . . . When I came...
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Inception of Gold
Lexy TimmsThings are not as bad as they seem. They are worse. Being the personal assistant to a narcissistic actress who just happens to own the key to my family's undoing isn't ex...
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Silver Santa
Lacey SilksTrapped together on Christmas, their unintended onenight stand becomes a lifechanging encounter amidst the snow. Laura Young's professional role as a security guard at the Sil...
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Good Guy
Kate MeaderHe's a Special Forces veteran making his pro hockey debut. She's a dogged sports reporter determined to get a scoop. She's also his best friend's widow . . . Fa...
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Rogue Alpha
Kimber WhiteOne touch made her crave him. But the pull of fate could be the path to ruin. College student Laura Prince lands a plum internship deep in the Michigan wilderness. When she discove...
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Pretty Little Lies
Ivy ThornFour years ago, Nicolo Marchetti took my innocence. But he left me with something else Nicolo almost took everything from me. My virginity, my reputation, and very nearly my future...
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Christmas in Sweetbriar Cove
Melody GraceCelebrate the holidays in Sweetbriar Cove with this festive romance collection, containing two sizzling smalltown holiday stories perfect for fans of Tessa Bailey, Sophie Kinsella...
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Bewitching a Highlander
Roma CordonDefying all for the love of a bewitching lass. Breena MacRae, a healer from Skye with a touch of witchery in her blood, embarks on a dangerous search for her missing father. She ar...
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The Count of Monte Cristo
Alexandre DumasAn Apple Books Classic edition. Alexandre Dumas’ classic paints a portrait of Edmond Dantès, a dark and calculating man who is willing to wait years to exact his perfect plan for r...
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Law of Attraction
Jordan HollisHow to Finally Overcome the Hurdles of Manifesting Proven, effective and enjoyable ways to help you manifest faster… Right now, think of something that makes you successful. If you...
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Enemies With Benefits
Roxie NoirI don’t love him. I don’t even like him. I just want him. Eli Loveless was my nemesis from the first day of kindergarten until we graduated high school. Everything I did, he had to...
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Little Women
Louisa May AlcottAn Apple Books Classic edition. Meet the Marches! Louisa May Alcott’s classic introduces us to four unforgettable sisters: beautiful Meg, tomboyish Jo, delicate Beth, and Amy, the ...
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The Stoic Mind
Addy Osmani & GoLimitlesssDiscover the timeless wisdom of Stoicism in a modern context with "The Stoic Mind," an enlightening visual guide by Addy Osmani and GoLimitlesss. This rich exploration co...
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The Icing on the Cake
Linda SeedShe’s a baker without a kitchen. He’s got a double oven to spare. It’s a recipe for success, until his mother starts stirring up trouble … Cassie Jordan has a sweet dream to open a...
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Noxious
Lexy TimmsStop setting yourself on fire to keep someone else warm. Brady and Levi have been together since high school, since before he became famous and started thinking only about himself....
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Dream Psychology
Sigmund FreudAn Apple Books Classic edition. Written by the founding father of psychoanalysis, Sigmund Freud’s 1899 book is the definitive text on learning to interpret dreams. Freud’s groundbr...