논문KCI 등재
Finite $p$-groups in which the normalizer of every non-normal subgroup is contained in its normal closure
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In this paper, finite $p$-groups $G$ satisfying $N_G(H)\leq H^G$ for every non-normal subgroup $H$ of $G$ are completely classified. This solves a problem proposed by Y. Berkovich.
Abstract
In this paper, finite $p$-groups $G$ satisfying $N_G(H)\leq H^G$ for every non-normal subgroup $H$ of $G$ are completely classified. This solves a problem proposed by Y. Berkovich.
참고문헌 (8)
- Y. Berkovich, "Groups of Prime Power Order. Vol. 1" (2008), Walter de Gruyter GmbH & Co. KG
- B. Huppert, "Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134" (1967), Springer-Verlag
- B. Huppert, "Finite groups. II, Grundlehren der Mathematischen Wis-senschaften, 242" (1982), Springer-Verlag
- H. Lv, "Some finite p-groups with bounded index of every cyclic subgroup in its normal closure", J. Algebra, 338, pp.169~179 (2011)
- L. Redei, "Das "schiefe Produkt" in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehoren", Comment. Math. Helv, 20, pp.225~264 (1947)
- M. Xu, "Finite p-groups all of whose non-abelian proper subgroups are generated by two elements", J. Algebra, 319(9), pp.3603~3620 (2008)
- X. Zhang, "Finite p-groups whose non-normal cyclic subgroups have small index in their normalizers", J. Group Theory, 15(5), pp.641~659 (2012)
- L. Zhao, "Finite p-groups in which the normal closures of the non-normal cyclic subgroups have small index", J. Algebra Appl, 13(2), pp.7~ (2014)
관련 논문AI추천
Finite $p$-groups whose normal closures of non-normal subgroups have two ordersLifang Wang대한수학회 · 대한수학회지2022 · 제59권 제4호FINITE p-GROUPS WHOSE NON-CENTRAL CYCLIC SUBGROUPS HAVE CYCLIC QUOTIENT GROUPS IN THEIR CENTRALIZERSHaipeng Qu, Jiao Wang, Lihua Zhang대한수학회 · 대한수학회보2015 · 제52권 제2호NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPSJuan Gao, Qinhai Zhang대한수학회 · 대한수학회지2012 · 제49권 제1호Finite groups which have many normal subgroupsHaipeng Qu, Mingyao Xu, Qinhai Zhang, Xiaoqiang Guo대한수학회 · 대한수학회지2009 · 제46권 제6호Finite $p$-groups all of whose subgroups of class 2 are generated by two elementsPujin Li, Qinhai Zhang대한수학회 · 대한수학회지2019 · 제56권 제3호A generalization of ${\mathcal A}_2$-groupsJunqiang Zhang대한수학회 · 대한수학회보2022 · 제59권 제4호
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