On conjugacy class sizes of primary and biprimary elements of a finite group

Let m, n 〉 1 be two coprime integers. In this paper, we prove that a finite solvable group is nilpotent if the set of the conjugacy class sizes of its primary and biprimary elements is {1, rn, n, mn}.

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Veröffentlicht in:	Science China. Mathematics 2014-03, Vol.57 (3), p.491-498
Hauptverfasser:	Shao, ChangGuo, Jiang, QinHui
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics China Integers Mathematical analysis Mathematics Mathematics and Statistics 互质元素共轭类尺寸幂零整数有限可解群有限群
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Beschreibung
Zusammenfassung:	Let m, n 〉 1 be two coprime integers. In this paper, we prove that a finite solvable group is nilpotent if the set of the conjugacy class sizes of its primary and biprimary elements is {1, rn, n, mn}.
ISSN:	1674-7283 1869-1862
DOI:	10.1007/s11425-013-4666-1