University of Isfahan International Journal of Group Theory 2251-7650 8 4 2019 12 01 The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups 1 3 23001 10.22108/ijgt.2018.110074.1472 EN Julian Brough Fachgruppe Mathematik und Informatik, BU Wuppertal, Wuppertal, Germany Journal Article 2018 03 08 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. https://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf