논문KCI 등재
Finite groups which are minimal with respect to s-quasinormality and self-normality
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An SQNS-group G is a group in which every proper sub- group of G is either s-quasinormal or self-normalizing and a minimal non-SQNS-group is a group which is not an SQNS-group but all of whose proper subgroups are SQNS-groups. In this note all the finite minimal non-SQNS-groups are determined.
Abstract
An SQNS-group G is a group in which every proper sub- group of G is either s-quasinormal or self-normalizing and a minimal non-SQNS-group is a group which is not an SQNS-group but all of whose proper subgroups are SQNS-groups. In this note all the finite minimal non-SQNS-groups are determined.
참고문헌 (8)
- K. Doerk, "Minimal nicht uberaufl osbare endliche Gruppen", Math. Z, 91, pp.198~205 (1966)
- D. Gorenstein, "Finite Groups" (1980), Harper & Row press
- P. Guo, "On minimal non-MSN-groups", Front. Math. China, 6(5), pp.847~854 (2011)
- H. Kurzweil, "The Theory of Finite Groups" (2004), Springer- Verlag
- T. J. Laffey, "A Lemma on finite p-group and some consequences", Proc. Cambridge Philos. Soc, 75, pp.133~137 (1974)
- K. Lu, "Finite groups with only s-quasinormal and self-normalzing subgroups", Soochow J. Math, 24(1), pp.9~12 (1998)
- G. A. Miller, "Non-abelian groups in which every subgroup is abelian", Trans. Amer. Math. Soc, 4(4), pp.398~404 (1903)
- J. G. Thompson, "Nonsolvable finite groups all of whose local subgroups are solvable", Bull. Amer. Math. Soc, 74, pp.383~437 (1968)
관련 논문AI추천
ON MINIMAL NON-QNS-GROUPSGuiyun Chen, Huaguo Shi, Zhangjia Han대한수학회 · 대한수학회보2014 · 제51권 제4호On minimal non-NSN-groupsGuiyun Chen, Huaguo Shi, Zhangjia Han대한수학회 · 대한수학회지2013 · 제50권 제3호Finite groups all of whose maximal subgroups are SB-groupsHailiang Zhang, Junxin Wang, Pengfei Guo대한수학회 · 대한수학회보2014 · 제51권 제4호Finite groups which have many normal subgroupsHaipeng Qu, Mingyao Xu, Qinhai Zhang, Xiaoqiang Guo대한수학회 · 대한수학회지2009 · 제46권 제6호Finite $p$-groups whose normal closures of non-normal subgroups have two ordersLifang Wang대한수학회 · 대한수학회지2022 · 제59권 제4호FINITE GROUPS WITH SOME SEMI-p-COVER-AVOIDING OR ss-QUASINORMAL SUBGROUPSQingjun Kong, Xiuyun Guo대한수학회 · 대한수학회보2014 · 제51권 제4호
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