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A generalization of ${\mathcal A}_2$-groups

Junqiang Zhang
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회보 (Bulletin of the KMS)|제59권 제4호|pp. 951-960|DOI 10.4134/BKMS.b210562

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참고문헌

키워드

maximal subgroupsFinite $p$-groupsminimal nonabelian subgroups
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초록

In this paper, we determine the finite $p$-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite $p$-group in which any two distinct ${\mathcal A}_1$-subgroups generate an ${\mathcal A}_2$-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.

Abstract

In this paper, we determine the finite $p$-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite $p$-group in which any two distinct ${\mathcal A}_1$-subgroups generate an ${\mathcal A}_2$-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.

참고문헌 (17)

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관련 논문AI추천

Finite $p$-groups all of whose subgroups of class 2 are generated by two elementsPujin Li, Qinhai Zhang대한수학회 · 대한수학회지2019 · 제56권 제3호Finite $p$-groups in which the normalizer of every non-normal subgroup is contained in its normal closureJunxin Wang, Pengfei Bai, Xiuyun Guo대한수학회 · 대한수학회보2018 · 제55권 제6호Finite $p$-groups whose normal closures of non-normal subgroups have two ordersLifang Wang대한수학회 · 대한수학회지2022 · 제59권 제4호FINITE p-GROUPS WHOSE NON-ABELIAN SUBGROUPS HAVE THE SAME CENTERLifang Wang대한수학회 · 대한수학회지2017 · 제54권 제4호FINITE p-GROUPS WHOSE NON-CENTRAL CYCLIC SUBGROUPS HAVE CYCLIC QUOTIENT GROUPS IN THEIR CENTRALIZERSHaipeng Qu, Jiao Wang, Lihua Zhang대한수학회 · 대한수학회보2015 · 제52권 제2호On finite barely non-abelian $p$-groupsDongSeung Kang대한수학회 · 대한수학회보2016 · 제53권 제5호

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