ON MINIMAL NON-NSN-GROUPS
ON MINIMAL NON-NSN-GROUPS
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DOI：
10.4134/jkms.2013.50.3.579
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发表时间：
2013-05
影响因子：
4.5
通讯作者：
Z. Han;Guiyun Chen;H. Shi
中科院分区：
文献类型：
--
作者：
Z. Han;Guiyun Chen;H. Shi
抽象。有限群G称为NSN-群，如果G的每个真子群在G中正规或自正规。本文确定了真子群均为NSN-群的非NSN-群。1.引论R对子群全正规的群（称为Dedekind群或Hamilton群）的结构进行了完全的艾德分类。Dedekind，E. Wendt和R.裸（见[9，定理5.3.7]）。从那时起，许多作者都对此类群体进行了概括。我们在这里提到其中的一些。Pic [8]考虑了每个子群S都是拟正规的有限群，即S对G的所有子群H都满足SH = HS，Walls [11]研究了Sylow子群的极大子群在G中正规的群。Buckley等[2]研究了子群至多形成两个共轭类的群，Brandl [1]研究了非正规子群都共轭的群，若N是G的正规子群，则N被G的所有元素正规化，对正规子群，G正规化N的元素个数最多为最大.另一方面，如果N
Abstract. A finite group Gis called an NSN-group if every proper sub-group of G is either normal in G or self-normalizing. In this paper, thenon-NSN-groups whose proper subgroups are all NSN-groups are deter-mined. 1. IntroductionThestructureofthe groupwhosesubgroupsareallnormal(calledaDedekindgroup or a Hamiltonian group) has been completely classified by R. Dedekind,E. Wendt and R. Bare (see [9, Theorem 5.3.7]). Since then, many authors havedealt with generalizations of such kind of groups. We mention some of themhere. Pic [8] considered finite groups in which every subgroup S is quasinor-mal, that is, S satisfies SH = HS for all subgroups H of G, and Walls [11]studied groups with maximal subgroups of Sylow subgroups that are normalin G. Buckley et al. [2] dealt with groups in which all subgroups form at mosttwo conjugate classes and Brandl [1] classified groups all of whose non-normalsubgroups are conjugates.If N is a normal subgroup of G, then N is normalized by all elements of G.For a normal subgroup, the number of elements of G normalizing N is up tomaximum. On the other hand, if N