FINITE GROUPS WITH SOME SEMI-p-COVER-AVOIDING OR ss-QUASINORMAL SUBGROUPS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 51, Issue 4, 2014, pp.943-948
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2014.51.4.943

Title & Authors

FINITE GROUPS WITH SOME SEMI-p-COVER-AVOIDING OR ss-QUASINORMAL SUBGROUPS

Kong, Qingjun; Guo, Xiuyun;

Kong, Qingjun; Guo, Xiuyun;

Abstract

Suppose that G is a finite group and H is a subgroup of G. H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is said to be semi-p-cover-avoiding in G if there is a chief series 1 = < < < of G such that, for every i = 1, 2, , t, if is a p-chief factor, then H either covers or avoids . We give the structure of a finite group G in which some subgroups of G with prime-power order are either semi-p-cover-avoiding or ss-quasinormal in G. Some known results are generalized.

Keywords

ss-quasinormal subgroup;semi-p-cover-avoiding subgroup;saturated formation;

Language

English

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