EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 98(112), pp. 265–270 (2015)

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Finite groups with three conjugacy class sizes of certain elements

Quinhui Jiang, Changguo Shao

School of Mathematics, University of Jinan, Shandong, China

Abstract: Let $G$ be a finite group and $m,n$ two positive coprime integers. We prove that the set of conjugacy class sizes of primary and biprimary elements of $G$ is $\{1,m,n\}$ if and only if $G$ is quasi-Frobenius with abelian kernel and complement.

Keywords: finite groups; conjugacy class sizes; primary and biprimary elements

Classification (MSC2000): 20D10; 20E45

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