Geodesic
Finite Groups with Three Conjugacy Class Sizes of Certain Elements
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 265 .

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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.
DOI : 10.2298/PIM140905001J
Classification : 20D10, 20E45
Keywords: finite groups, conjugacy class sizes, primary and biprimary elements 
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     author = {Quinhui Jiang and Changguo Shao},
     title = {Finite {Groups} with {Three} {Conjugacy} {Class} {Sizes} of {Certain} {Elements}},
     journal = {Publications de l'Institut Math\'ematique},
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Quinhui Jiang; Changguo Shao. Finite Groups with Three Conjugacy Class Sizes of Certain Elements. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 265 . doi : 10.2298/PIM140905001J. http://geodesic.mathdoc.fr/articles/10.2298/PIM140905001J/

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