General introduction to the special odd case General lemmas Theorem $C^*_2$: Stage 1 Theorem $C^*_2$: Stage 2 Theorem $C_2$: Stage 3 Theorem $C_2$: Stage 4 Theorem $C_2$: Stage 5 Theorem $C_3$: Stage 1 Theorem $C_3$: Stages 2 and 3 IV$_K$: Preliminary properties of $K$-groups Background references Expository references Glossary Index.

http://inis.jinr.ru/sl/M_Mathematics/MA_Algebra/MAtg_Group%20theory/Gorenstein%20D.,%20Lyons%20R.,%20Solomon%20R.%20Classification%20of%20finite%20simple%20groups%201%20(AMS%20survey%2040%20no.1,%201994,%202000)(176s).pdf

The Classification of the Finite Simple Groups

Finite Generalized Quadrangles

/pdf/nonsolvable-finite-groups-all-of-whose-local-subgroups-are-2gfzytcj61.pdf

Nonsolvable finite groups all of whose local subgroups are solvable

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/22240/0000676.pdf;sequence=1

On the minimal degrees of projective representations of the finite Chevalley groups

We define and study sl2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show

http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n1-p05.pdf

Derived equivalences for symmetric groups and sl2-categorification

The blocks of finite general linear and unitary groups

Weights for symmetric and general linear groups

In this paper we study the blocks of a finite classical group for primes r unequal to the defining characteristic p of the group, where r and p are odd primes. The relevant finite classical groups are groups of fixed points G of Frobenius endomorphisms F of classical algebraic groups G with connected centers. So G is a conformal symplectic or orthogonal group in even dimension, or a special orthogonal group in odd dimension, that is, one of the groups CSp(2w, q\\ CSO(2n,q\\ or SO(2n 4-1, #). The irreducible characters of these groups have been classified by Lusztig in [10]. In particular, his results imply a Jordan decomposition of the irreducible characters by pairs (5, /l), where s is a representative of a semisimple conjugacy class of the dual group G*, and is a unipotent character of (CG*(s))*. Our results imply a similar Jordan decomposition for blocks. Indeed, let us define a unipotent block to be a block containing a unipotent character. Then the blocks of G are labeled by pairs (s, ), where s is a representative of a semisimple r'-conjugacy class of G*, and : is a unipotent block of (CG*(s))*. These results are thus similar to those for blocks of general linear groups and unitary groups studied in [8], where the language of partitions, hooks, and cores allowed a combinatorial formulation for the classification of characters into blocks. In the present paper, a similar combinatorial formulation for the classification of characters into blocks is given äs well.

The blocks of finite classical groups.

Publisher Summary A group G is said to have a (B, N)-pair if there exist subgroups B and N of G satisfying the conditions: (1) G =

Paul Fong

Papers

The blocks of finite general linear and unitary groups

Weights for symmetric and general linear groups

The blocks of finite classical groups.

Groups with a (B, N)-Pair of Rank 2. I

Brauer trees in classical groups