Non-vanishing elements in finite groups

2016/03/13 by Brough, Julian
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1603.04051

Abstract

Many results have been established about determining whether or not an element evaluates to zero on an irreducible character of a group. In this note it is shown that if a group G has a normal nilpotent subgroup N, and P is a Sylow p-subgroup of G, then no irreducible character of G vanishes on N∩ Z(P).

Related

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• On common zeros of characters of finite groups
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• Vanishing Elements of Prime Power Order
• On vanishing criteria that control finite group structure