$\tau$-primitive subgroups of finite groups

N. Yang, W. Guo

Department of Mathematics, Xuzhou Normal University, Xuzhou, P. R. China

Abstract: We study the influence of $\tau$-primitive subgroups on the structure of finite groups. As applications, we give the structure of the finite groups whose every subgroup is an intersection of subgroups of prime power index and the structure of finite groups whose every subnormal subgroup is an intersection of subnormal subgroups of prime power index.

Keywords: finite group, subgroup functor, $\tau$-primitive subgroup, $X$-permutable subgroup, group structure.

UDC: 512.54

Received: 27.08.2007

 English version: Siberian Mathematical Journal, 2009, 50:3, 560–566

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