Groups having complete bipartite divisor graphs for their conjugacy class sizes
Group Theory
2013-09-24 v1 Combinatorics
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)\neq 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.
Cite
@article{arxiv.1309.5629,
title = {Groups having complete bipartite divisor graphs for their conjugacy class sizes},
author = {Roghayeh Hafezieh and Pablo Spiga},
journal= {arXiv preprint arXiv:1309.5629},
year = {2013}
}
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5 pages