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

Kong, Qingjun;Guo, Xiuyun

• Published : 2014.07.31
• 35 5

#### 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 = $G_0$ < $G_1$ < ${\cdots}$ < $G_t=G$ of G such that, for every i = 1, 2, ${\ldots}$, t, if $G_i/G_{i-1}$ is a p-chief factor, then H either covers or avoids $G_i/G_{i-1}$. 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

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