University of IsfahanInternational Journal of Group Theory2251-76508420191201The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups132300110.22108/ijgt.2018.110074.1472ENJulian BroughFachgruppe Mathematik und Informatik, BU Wuppertal, Wuppertal, GermanyJournal Article20180308We 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.http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf