Jianbei An

Weights for classical groups

This paper proves the Alperins weight conjecture for the finite unitary groups when the characteristic r of modular representation is odd. Moreover, this paper proves the conjecture for finite odd dimensional special orthogonal groups and gives a combinatorial way to count the number of weights, block by block, for finite symplectic and even dimensional special orthogonal groups when r and the defining characteristic of the groups are odd.

The alperin and dade conjectures for the simple mathieu groups

This paper is part of a program to study Alperin’s weight conjecture and Dade’s conjecture on counting characters in blocks for several finite groups. The local structures of radical subgroups and certain radical chains in the simple Mathieu groups are given, and the conjectures are confirmed for these groups.

The Alperin Weight Conjecture and Dade's Conjecture for the simple group Fi'24

We classify the radical p -subgroups and chains of the Fischer simple group Fi′ 24 and then verify the Alperin weight conjecture and the Uno reductive conjecture for Fi′ 24 .

2-weights for unitary groups

This paper gives a description of the local structures of 2-radical subgroups in a finite unitary group and proves Alperins weight conjecture for finite unitary groups when the characteristic of modular representation is even

THE ALPERIN WEIGHT CONJECTURE AND UNO'S CONJECTURE FOR THE BABY MONSTER B, p ODD

Suppose that p is 3, 5 or 7. In this paper, faithful permutation representations of maximal p-local subgroups are constructed, and the radical p-chains of the Baby Monster B are classified. Hence, the Alperin weight conjecture and the Uno reductive conjecture can be verified for B, the latter being a refinement of Dade’s reductive conjecture and the Isaacs–Navarro conjecture.

Conjectures on the character degrees of the harada-norton simple group HN

We classify the radical subgroups and chains of the Harada-Norton simple group HN and verify the Alperin weight conjecture and the refined Dade conjecture due to Uno for the group. This implies the Isaacs-Navarro and Dade reductive conjectures for the group.

Nilpotent blocks of quasisimple groups for odd primes

Abstract We investigate the nilpotent blocks of positive defect of the quasisimple groups for odd primes. In particular, it is shown that every nilpotent block of a quasisimple group has abelian defect groups. A conjecture of Puig concerning the recognition of nilpotent blocks is also shown for these groups.

The Alperin and dade conjectures for the simple Conway’s third group

This paper is part of a program to study Alperin’s weight conjecture and Dade’s conjecture on counting ordinary characters in blocks for several finite groups. The classifications of radical subgroups and certain radical chains and their local structures of the simple Conway’s third group have been obtained by using the computer algebra system CAYLEY. The Alperin weight conjecture and the Dade final conjecture have been confirmed for the group.

The Alperin weight conjecture and Uno's conjecture for the Monster M, p odd

Suppose that p is 3, 5 or 7. In this paper, faithful permutation representations of maximal p-local subgroups are constructed, and the radical p-chains of the Baby Monster B are classified. Hence, the Alperin weight conjecture and the Uno reductive conjecture can be verified for B, the latter being a refinement of Dade’s reductive conjecture and the Isaacs–Navarro conjecture.

The Alperin and Dade Conjectures for the Conway Simple Group Co1

We classify the radical subgroups and chains of the Conway simple group Co1 and then verify the Alperin weight conjecture and the Dade final conjecture for this group.