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Finite groups which have many normal subgroups
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In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.
Abstract
In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.
참고문헌 (9)
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- D. Gorenstein, "The Classification of the Finite Simple Groups. Number 6. Part IV, The special odd case. Mathematical Surveys and Monographs, 40.6", American Mathematical Society, Providence, ~ (2005)
- B. Huppert, "Endliche Gruppen I" (1967), Springer-Verlag
- H. Kurzweil, "The Theory of Finite Groups" (2004), Springer
- D. S. Passman, "Nonnormal subgroups of p-groups", J. Algebra, 15, pp.352~370 (1970)
- L. R´edei, "Das schiefe Product in der Gruppentheorie", Comment. Math. Helvet., 20, pp.225~267 (1947)
- M. Xu, "Finite p-groups all of whose subgroups of index p2 are metacyclic", ~
- Q. Zhang, "Finite groups whose nontrivial normal subgroups have the same order", J. Math. Res. Exposition, 28(4), pp.807~812 (2008)
관련 논문AI추천
Finite $p$-groups whose normal closures of non-normal subgroups have two ordersLifang Wang대한수학회 · 대한수학회지2022 · 제59권 제4호Finite $p$-groups in which the normalizer of every non-normal subgroup is contained in its normal closureJunxin Wang, Pengfei Bai, Xiuyun Guo대한수학회 · 대한수학회보2018 · 제55권 제6호Finite groups all of whose maximal subgroups are SB-groupsHailiang Zhang, Junxin Wang, Pengfei Guo대한수학회 · 대한수학회보2014 · 제51권 제4호ON MINIMAL NON-QNS-GROUPSGuiyun Chen, Huaguo Shi, Zhangjia Han대한수학회 · 대한수학회보2014 · 제51권 제4호FINITE p-GROUPS WHOSE NON-ABELIAN SUBGROUPS HAVE THE SAME CENTERLifang Wang대한수학회 · 대한수학회지2017 · 제54권 제4호Finite groups which are minimal with respect to s-quasinormality and self-normalityHuagui Shi, Wei Zhou, Zhangjia Han대한수학회 · 대한수학회보2013 · 제50권 제6호
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