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FINITE p-GROUPS WHOSE NON-ABELIAN SUBGROUPS HAVE THE SAME CENTER

Lifang Wang
대한수학회 (The Korean Mathematical Society)|2017.07|대한수학회지 (Journal of the KMS)|제54권 제4호|pp. 1109-1120

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참고문헌

키워드

minimal non-abelian groups$\mathcal{A}_2$-groupsthe center of a group
주제분류수학

초록

For an odd prime $p$, finite $p$-groups whose non-abelian subgroups have the same center are classified in this paper.

Abstract

For an odd prime $p$, finite $p$-groups whose non-abelian subgroups have the same center are classified in this paper.

참고문헌 (13)

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  2. A. A. Finogenov, "On finite p-groups with a cyclic commutator group and cyclic center", Math. Notes, 63(5-6), pp.802~812 (1998)
  3. B. Huppert, "Endliche Gruppen I" (1967), Springer-Verlag
  4. Z. Janko, "Finite nonabelian p-groups having exactly one maximal subgroup with a noncyclic center", Arch. Math. (Basel), 96(2), pp.101~103 (2011)
  5. M. F. Newman, "Metacyclic groups of prime-power order", ~ (1987)
  6. 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. Helvet, 20, pp.225~264 (1947)
  7. H. F. Tuan, "A theorem about p-groups with abelian subgroup of index p", Acad Sinica Science Record, 3, pp.17~23 (1950)
  8. L. F. Wang, "Finite 2-groups whose non-abelian subgroups have the same Center", J. Group Theory, 17(4), pp.689~703 (2014)
  9. M. Y. Xu, "A theorem on metabelian p-groups and some consequences", Chin. Ann. Math, 5B, pp.1~6 (1984)
  10. M. Y. Xu, "Finite p-groups all of whose non-abelian proper subgroups are generated by two elements", J. Algebra, 319(9), pp.3603~3620 (2008)
  11. M. Y. Xu, "A classification of metacyclic 2-groups", Algebra Colloq, 13(1), pp.25~34 (2006)
  12. Q. H. Zhang, "Finite p-groups all of whose subgroups of index p2 are abelian", Algebra Colloq, 15(1), pp.167~180 (2008)
  13. Q. H. Zhang, "Finite p-groups all of whose subgroups of index p3 are abelian", Commun. Math. Stat, 3(1), pp.69~162 (2015)

관련 논문AI추천

Finite $p$-groups whose normal closures of non-normal subgroups have two ordersLifang Wang대한수학회 · 대한수학회지2022 · 제59권 제4호On finite barely non-abelian $p$-groupsDongSeung Kang대한수학회 · 대한수학회보2016 · 제53권 제5호FINITE p-GROUPS WHOSE NON-CENTRAL CYCLIC SUBGROUPS HAVE CYCLIC QUOTIENT GROUPS IN THEIR CENTRALIZERSHaipeng Qu, Jiao Wang, Lihua Zhang대한수학회 · 대한수학회보2015 · 제52권 제2호Finite groups which have many normal subgroupsHaipeng Qu, Mingyao Xu, Qinhai Zhang, Xiaoqiang Guo대한수학회 · 대한수학회지2009 · 제46권 제6호Finite $p$-groups in which the normalizer of every non-normal subgroup is contained in its normal closureJunxin Wang, Pengfei Bai, Xiuyun Guo대한수학회 · 대한수학회보2018 · 제55권 제6호A generalization of ${\mathcal A}_2$-groupsJunqiang Zhang대한수학회 · 대한수학회보2022 · 제59권 제4호

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