A solution to Brauer's Problem 14

2022/12/16 by Murray, John, Sambale, Benjamin
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2212.08357

Abstract

It is well known that the number of real irreducible characters of a finite group G coincides with the number of real conjugacy classes of G. Richard Brauer has asked if the number of irreducible characters with Frobenius-Schur indicator 1 can also be expressed in group theoretical terms. We show that this can done by counting solutions of g₁²… g_n²=1 with g₁,…,g_n∈ G.

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