Order three normalizers of 2-groups

2016/05/11 by Spencer Gerhardt, Gerhardt, Spencer
Mathematics · #20E99 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E99

paper · pdf · doi:10.48550/arxiv.1605.03257

14 pages; to appear in Communications in Algebra

arxiv created 2016/10/21 · arxiv updated 2016/10/25

Abstract

This paper examines order three elements of finite groups which normalize no nontrivial 2-subgroup. The motivation for finding such elements arises out of a problem in modular representation theory. The question of when these elements appear in the almost simple groups was posed by Geoff Robinson in the context of studying 2-blocks of defect zero. For the almost simple groups, a complete classification of order three elements with this property is determined. On the basis of this result, necessary conditions are then given for the existence of such elements in a large class of finite groups.

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