JournalsrsmupVol. 133pp. 117–123

Groups having complete bipartite divisor graphs for their conjugacy class sizes

  • Roghayeh Hafezieh

    Gebze Institute of Technology, Turkey
  • Pablo Spiga

    Università degli Studi di Milano-Bicocca, Italy
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Abstract

Given a finite group GG, the bipartite divisor graph for its conjugacy class sizes is the bipartite graph with bipartition consisting of the set of conjugacy class sizes of GZ(G)G\setminus\mathbf Z (G) (where Z(G)\mathbf Z (G) denotes the centre of GG) and the set of prime numbers that divide these conjugacy class sizes, and with {p,n}\{p,n\} being an edge if gcd(p,n)1(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 K2,5K_{2,5}, giving a solution to a question of Taeri [15].

Cite this article

Roghayeh Hafezieh, Pablo Spiga, Groups having complete bipartite divisor graphs for their conjugacy class sizes. Rend. Sem. Mat. Univ. Padova 133 (2015), pp. 117–123

DOI 10.4171/RSMUP/133-6