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arXiv · 1307.5780

Supports of irreducible characters of p-groups

Tom Wilde
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Abstract

If chi is an irreducible character of a finite group G then the support of chi is the subset of G on which chi does not vanish. In this note, we study the supports of characters of certain classes of p-groups (a p-group is a finite group of prime power order). We show that if chi is an irreducible character of a metabelian p-group P, then the support of chi contains at most |P|/chi(1)^2 conjugacy classes, and we give a bound on the orders of the elements in the support. We give more precise results for p-groups of nilpotence class at most 3 and groups of order dividing p^9.

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Tom Wilde. 2013-07-22. Supports of irreducible characters of p-groups. https://arxiv.org/abs/1307.5780

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