The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups

Document Type : Research Paper


Fachgruppe Mathematik und Informatik, BU Wuppertal, Wuppertal, Germany


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.


Main Subjects

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  • Receive Date: 08 March 2018
  • Revise Date: 29 May 2018
  • Accept Date: 16 October 2018
  • Published Online: 01 December 2019