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European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
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133
2015
0
Groups having complete bipartite divisor graphs for their conjugacy class sizes
Roghayeh
Hafezieh
Gebze Institute of Technology, GEBZE, TURKEY
Pablo
Spiga
Università degli Studi di Milano-Bicocca, MILANO, ITALY
Bipartite divisor graph, conjugacy class size, extra-special group
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 $G\setminus\mathbf Z (G)$ (where $\mathbf Z (G)$ 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 [15].
General
117
123
10.4171/RSMUP/133-6
http://www.ems-ph.org/doi/10.4171/RSMUP/133-6