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arXiv · 1605.03257

Order three normalizers of 2-groups

Spencer Gerhardt
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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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Spencer Gerhardt. 2016-10-21. Order three normalizers of 2-groups. https://arxiv.org/abs/1605.03257

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