Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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FINITE GROUPS WITH SOME SEMI-p-COVER-AVOIDING OR ss-QUASINORMAL SUBGROUPS

  • Kong, Qingjun (Department of Mathematics Tianjin Polytechnic University) ;
  • Guo, Xiuyun (Department of Mathematics Shanghai University)
  • Received : 2013.06.11
  • Published : 2014.07.31
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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.

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References

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