Suppose that H is a subgroup of a finite group G. H is called ?-quasinormal in G if it permutes with every Sylow subgroup of G; H is called ?-quasinormally embedded in G provided every Sylow subgroup of H is a Sylow subgroup of some ?-quasinormal subgroup of G; H is called csupplemented in G if there exists a subgroup N of G such that G = HN and H ∩ N ≤ HG = CoreG(H). In this paper, finite groups G satisfying the condition that some kinds of subgroups of G are either ?-quasinormally embedded or c-supplemented in G, are investigated, and theorems which unify some recent results are given.
LI Yangming, PENG Kangtai
. -quasinormally
embedded and c-supplemented subgroup of finite group[J]. Frontiers of Mathematics in China, 2008
, 3(4)
: 511
-521
.
DOI: 10.1007/s11464-008-0037-6
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