Groups having complete bipartite divisor graphs for their conjugacy class sizes

2013/09/22 by Hafezieh, Roghayeh, Spiga, Pablo
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1309.5629

Abstract

Given a finite group G, the bipartite divisor graph for its conjugacy class sizes is the bipartite graph with bipartition consisting of the set of conjugacy class sizes of G-Z (where Z denotes the centre of G) and the set of prime numbers that divide these conjugacy class sizes, and with p,n being an edge if gcd(p,n)≠ 1. In this paper we construct infinitely many groups whose bipartite divisor graph for their conjugacy class sizes is the complete bipartite graph K_2,5, giving a solution to a question of Taeri.

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