School of Mathematics & Physics, University of Lincoln
New paper by Evgeny Khukhro (Univ. of Lincoln), Alexander Moretó (Univ. of Valencia, Spain), and Mohammad Zarrin (Univ. of Kurdistan, Iran), “The average element order and the number of conjugacy classes of finite groups” has been accepted for publication in Journal of Algebra. The work was supported by Mathematical Center in Akademgorodok, Ministerio de Ciencia e Innovación PID-2019-103854GB-100 and FEDER funds.
Abstract: Let be the average order of the elements of , where is a finite group. We show that there is no polynomial lower bound for in terms of , where , even when is a prime-power order group and is abelian. This gives a negative answer to a question of A. Jaikin-Zapirain.