Class Covering Numbers of Finite Simple Groups
โ Scribed by D. Alvis; M. Barry
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 185 KB
- Volume
- 162
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For a finite group G, let k G denote the number of conjugacy classes of G. We prove that a simple group of Lie type of untwisted rank l over the field of q ลฝ . l elements has at most 6 q conjugacy classes. Using this estimate we show that for ลฝ . ลฝ . 10 n completely reducible subgroups G of GL n, q
We construct a family F F of Frobenius groups having abelian Sylow subgroups ลฝ and non-inner, class-preserving automorphisms. We show that any A-group that is, . a finite solvable group with abelian Sylow subgroups has a sub-quotient belonging to F F provided it has a non-inner, class-preserving aut
For each finite simple group G there is a conjugacy class C such that each G nontrivial element of G generates G together with any of more than 1r10 of the members of C . Precise asymptotic results are obtained for the probability implicit G in this assertion. Similar results are obtained for almost