139 research outputs found
On 2-groups of almost maximal class
Let G be a 2-group of order 2^n, n>5, and nilpotency class n-2. The
invariants of such groups determined by their group algebras over the field of
two elements are given in the paper.Comment: 25 page
The Largest Irreducible Representations of Simple Groups
Answering a question of I. M. Isaacs, we show that the largest degree of
irreducible complex representations of any finite non-abelian simple group can
be bounded in terms of the smaller degrees. We also study the asymptotic
behavior of this largest degree for finite groups of Lie type. Moreover, we
show that for groups of Lie type, the Steinberg character has largest degree
among all unipotent characters.Comment: 34 page
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