| Twelve Sporadic Groups 1998 Edition Contributor(s): Griess, Robert L. Jr. (Author) |
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ISBN: 3540627782 ISBN-13: 9783540627784 Publisher: Springer OUR PRICE: $80.74 Product Type: Hardcover - Other Formats Published: August 1998 Annotation: The finite simple groups come in several infinite families (alternating groups and the groups of Lie type) plus 26 sporadic groups. The sporadic groups, discovered between 1861 and 1975, exist because of special combinatorial or arithmetic circumstances. A single theme does not capture them all. Nevertheless, certain themes dominate. The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. A leisurely and rigorous study of two of their three generations is the purpose of this book. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists. |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Algebra - Abstract |
| Dewey: 512.2 |
| LCCN: 98018097 |
| Series: Springer Monographs in Mathematics |
| Physical Information: 0.44" H x 6.14" W x 9.21" (0.95 lbs) 169 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |