%0 Journal Article
%T One-prime power hypothesis for conjugacy class sizes
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Camina, Alan
%A Camina, Rachel
%D 2017
%\ 09/01/2017
%V 6
%N 3
%P 13-19
%! One-prime power hypothesis for conjugacy class sizes
%K conjugacy class sizes
%K Finite groups
%K insoluble groups
%K bipartite graph
%R 10.22108/ijgt.2017.12043
%X A finite group $G$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to $S \times A$ where $A$ is abelian and $S \cong PSL_2(q)$ for $q \in {4,8}$. We confirm this conjecture.
%U https://ijgt.ui.ac.ir/article_12043_81116a607ca09117e53c05589eda4c89.pdf