%0 Journal Article
%T The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Brough, Julian
%D 2019
%\ 12/01/2019
%V 8
%N 4
%P 1-3
%! The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
%K Conjugacy classes
%K finite groups
%K restriction to substructures
%R 10.22108/ijgt.2018.110074.1472
%X We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers. Insoluble groups which satisfy the one-prime power hypothesis have been classified. However it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups. In this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups.
%U http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf