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Twelve Sporadic Groups (Springer Monographs in Mathematics)

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en Limba Engleză Hardback – 19 Aug 1998
The finite simple groups are basic objects in algebra since many questions about general finite groups can be reduced to questions about the simple groups. Finite simple groups occur naturally in certain infinite families, but not so for all of them: the exceptions are called sporadic groups, a term used in the classic book of Burnside [Bur] to refer to the five Mathieu groups. There are twenty six sporadic groups, not definitively organized by any simple theme. The largest of these is the monster, the simple group of Fischer and Griess, and twenty of the sporadic groups are involved in the monster as subquotients. These twenty constitute the Happy Family, and they occur naturally in three generations. In this book, we treat the twelve sporadics in the first two generations. I like these twelve simple groups very much, so have chosen an exposition to appreciate their beauty, linger on details and develop unifying themes in their structure theory. Most of our book is accessible to someone with a basic graduate course in abstract algebra and a little experience with group theory, especially with permu­ tation groups and matrix groups. In fact, this book has been used as the basis for second-year graduate courses.
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Specificații

ISBN-13: 9783540627784
ISBN-10: 3540627782
Pagini: 180
Dimensiuni: 156 x 234 x 15 mm
Greutate: 0.96 kg
Ediția: 1998
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării: Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

1. Background from General Group Theory.- 2. Assumed Results about Particular Groups.- 3. Codes.- 4. The Hexacode.- 5. The Golay Code.- 6. Subgroups of M24.- 7. The Ternary Golay Code and 2·M12.- 8. Lattices.- 9. The Leech Lattice and Conway Groups.- 10. Subgroups of the Conway Groups; the Simple Groups of Higman-Sims, McLaughlin, Hall-Janko and Suzuki; Local Subgroups; Conjugacy Classes.- 11. Generation Three of the Happy Family and the Pariahs.- Appendix. Some Comments on the Atlas.- References.- List of Group Theoretic Notations.- The Orders of the Finite Simple Groups.