This is proved by induction on 7n. For ni = 0 (\*) follows immediately from the definitions. Now take a E C,:,,, for m > 0. There is c E B,,,, such t'hat ac E pCp,n,-l + + C,,;f,l+l. There is thus a' E Cl~.flr-l with a E c + pa' + Cl,.,,f+l. By induction hypothesis a' E 6' + C,.,,, for some b' E @ B
Elementary Abelian 3-Subgroups of the Monster
β Scribed by Thomas M. Richardson
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 297 KB
- Volume
- 210
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
We classify the maximal elementary abelian 3-subgroups of the Monster simple group. There are 17 conjugacy classes of such subgroups. Fifteen of the classes have groups of order 3 7 , and the other classes have groups of order 3 6 and 3 8 . The classification uses the construction of 3-local subgroups of the Monster from [3].
π SIMILAR VOLUMES
We use our computer construction of the Monster sporadic simple group to find a new maximal subgroup PGL 2 (29). In particular, we prove containment of L 2 (29) in , thereby answering a long-standing open question.
Let p be a prime number and K be an algebraically closed field of characteristic p. Let G be a finite group and B be a (p-) block of G. We denote by l B the number of isomorphism classes of irreducible KG-modules in B. Let D be a defect group of B and let B 0 be the Brauer correspondent of B, that i
In representation theory of finite groups, there is a well-known and important conjecture due to M. BrouΓ©. He conjectures that, for any prime p, if a finite group G has an abelian Sylow p-subgroup P, then the derived categories of the principal p-blocks of G and of the normalizer N G P of P in G are