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1. |
Record Nr. |
UNINA9910970915503321 |
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Autore |
Li Cai-Heng |
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Titolo |
Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2022 |
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©2022 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (112 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.279 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Finite groups |
Group theory |
Group theory and generalizations -- Abstract finite groups -- Products of subgroups |
Group theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie type |
Group theory and generalizations -- Abstract finite groups -- Simple groups: sporadic groups |
Combinatorics -- Algebraic combinatorics -- Group actions on combinatorial structures |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Cover -- Title page -- Chapter 1. Introduction -- 1.1. Factorizations of almost simple groups -- 1.2. -Arc-transitive Cayley graphs -- 1.3. Discussions and some open problems -- Chapter 2. Preliminaries -- 2.1. Notation -- 2.2. Results on finite simple groups -- 2.3. Elementary facts concerning factorizations -- 2.4. Maximal factorizations of almost simple groups -- Chapter 3. The factorizations of linear and unitary groups of prime dimension -- 3.1. Singer cycles -- 3.2. Linear groups of prime dimension -- 3.3. Unitary groups of prime dimension -- Chapter 4. Non-classical groups -- 4.1. The case that both factors are solvable -- 4.2. Exceptional groups of Lie type -- 4.3. Alternating group socles -- 4.4. Sporadic group socles -- Chapter 5. Examples in classical groups -- 5.1. Examples in unitary groups -- 5.2. Examples in |
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symplectic groups -- 5.3. Examples in orthogonal groups of odd dimension -- 5.4. Examples in orthogonal groups of plus type -- Chapter 6. Reduction for classical groups -- 6.1. Inductive hypothesis -- 6.2. The case that has at least two non-solvable composition factors -- Chapter 7. Proof of Theorem 1.1 -- 7.1. Linear groups -- 7.2. Symplectic Groups -- 7.3. Unitary Groups -- 7.4. Orthogonal groups of odd dimension -- 7.5. Orthogonal groups of even dimension -- 7.6. Completion of the proof -- Chapter 8. -Arc-transitive Cayley graphs of solvable groups -- 8.1. Preliminaries -- 8.2. A property of finite simple groups -- 8.3. Reduction to affine and almost simple groups -- 8.4. Proof of Theorem 1.3 and Corollary 1.5 -- Appendix A. Tables for nontrivial maximal factorizations of almost simple classical groups -- Bibliography -- Back Cover. |
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Sommario/riassunto |
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"A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these nontrivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type. The characterization is then applied to study s-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary that, except for cycles, a non-bipartite connected 3-arc-transitive Cayley graph of a finite solvable group is necessarily a normal cover of the Petersen graph or the Hoffman-Singleton graph"-- |
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2. |
Record Nr. |
UNINA9910962478103321 |
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Autore |
Carlin Martha |
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Titolo |
Lost letters of medieval life : English society, 1200-1250 / / edited and translated by Martha Carlin and David Crouch |
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Pubbl/distr/stampa |
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Philadelphia, : University of Pennsylvania Press, c2013 |
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ISBN |
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9780812223361 |
0812223365 |
9780812207569 |
0812207564 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (361 p.) |
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Collana |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Letter writing |
England Civilization 1066-1485 Sources |
England Social life and customs 1066-1485 Sources |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (p. 293-319) and index. |
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Nota di contenuto |
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Front matter -- CONTENTS -- ILLUSTRATIONS -- Preface -- Abbreviations -- A Note on Money -- INTRODUCTION -- Chapter 1. Money -- Chapter 2. War and Politics -- Chapter 3. Lordship and Administration -- Chapter 4. Family and Community -- Chapter 5. A Knight's Correspondence: Building a Barn and a Windmill -- Bibliography -- General Index -- Subject Index -- ACKNOWLEDGMENTS |
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Sommario/riassunto |
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Everyday life in early thirteenth-century England is revealed in vivid detail in this riveting collection of correspondence of people from all classes, from peasants and shopkeepers to bishops and earls. The documents presented here include letters between masters and servants, husbands and wives, neighbors and enemies, and cover a wide range of topics: politics and war, going to fairs and going to law, attending tournaments and stocking a game park, borrowing cash and doing favors for friends, investigating adultery and building a windmill. While letters by celebrated people have long been known, the correspondence of ordinary people has not survived and has generally been assumed never to have existed in the first place. Martha Carlin |
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and David Crouch, however, have discovered numerous examples of such correspondence hiding in plain sight. The letters can be found in manuscripts called formularies-the collections of form letters and other model documents that for centuries were used to teach the arts of letter-writing and keeping accounts. The writing-masters and their students who produced these books compiled examples of all the kinds of correspondence that people of means, members of the clergy, and those who handled their affairs might expect to encounter in their business and personal lives. Tucked among the sample letters from popes to bishops and from kings to sheriffs are examples of a much more casual, ephemeral kind of correspondence. These are the low-level letters that evidently were widely exchanged, but were often discarded because they were not considered to be of lasting importance. Two manuscripts, one in the British Library and the other in the Bodleian Library, are especially rich in such documents, and it is from these collections that Carlin and Crouch have drawn the documents in this volume. They are presented here in their first printed edition, both in the original Latin and in English translation, each document splendidly contextualized in an accompanying essay. |
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