Orders of units in integral group rings and blocks of defect 1

2019/06/09 by Caicedo, Mauricio, Margolis, Leo
#05E10 #16U60 #20C05 #20C20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1906.03570

Abstract

We show that if the Sylow p-subgroup of a finite group G is of order p, then the normalized unit group of the integral group ring of G contains a normalized unit of order pq if and only if G contains an element of order pq, where q is any prime. We use this result to answer the Prime Graph Question for most sporadic simple groups and some simple groups of Lie type, including a new infinite series of such groups. Our methods are based on the understanding of blocks of cyclic defect and Young tableaux combinatorics.

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