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Broué's abelian defect group conjecture holds for the Harada–Norton sporadic simple group HN
Abstract In representation theory of finite groups, there is a well-known and important conjecture due to M. Broue. He conjectures that, for any prime p, if a p-block A of a finite group G has anExpand
Brou\'e's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group
In the representation theory of finite groups, there is a well-known and important conjecture, due to Brou\'e saying that for any prime p, if a p-block A of a finite group G has an abelian defectExpand
Vertices of Lie modules
Abstract Let Lie F ( n ) be the Lie module of the symmetric group S n over a field F of characteristic p > 0 , that is, Lie F ( n ) is the left ideal of F S n generated by the Dynkin–Specht–WeverExpand
On p-groups of Gorenstein-Kulkarni type
A finite p-group is said to be of Gorenstein-Kulkarni type if the set of all elements of non-maximal order is a maximal subgroup. 2-groups of Gorenstein-Kulkarni type arise naturally in the study ofExpand
Regular orbits of sporadic simple groups
Abstract Given a finite group G and a faithful irreducible FG-module V where F has prime order, does G have a regular orbit on V? This problem is equivalent to determining which primitive permutationExpand
Brou\'e's abelian defect group conjecture for the sporadic simple Janko group J_4 revisited
We show that the 3-block of the sporadic simple Janko group J_4 with defect group C_3 x C_3, and the principal 3-block of the alternating group A_8 are Puig equivalent, answering a question posed inExpand
Mixing operators with non-perfectly spanning unimodular eigenvectors.
For arbitrary closed countable subsets $Z$ of the unit circle examples of topologically mixing operators on Hilbert spaces are given which have a densely spanning set of unimodular eigenvectors withExpand
The Brauer characters of the sporadic simple Harada-Norton group and its automorphism group in characteristics 2 and 3
We determine the 2-modular and 3-modular character tables of the sporadic simple Harada-Norton group and its automorphism group.
On low-degree representations of the symmetric group
The aim of the present paper is to obtain a classification of all the irreducible modular representations of the symmetric group on n letters of dimension at most n, including dimension formulae.Expand
Source Algebras of Blocks, Sources of Simple Modules, and a Conjecture of Feit
Abstract We verify a finiteness conjecture of Feit on sources of simple modules over group algebras for various classes of finite groups related to the symmetric groups.
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