共查询到20条相似文献,搜索用时 31 毫秒
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Gangyong Lee 《代数通讯》2013,41(10):4077-4094
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Viktoria A. Kovaleva 《代数通讯》2013,41(12):5410-5415
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A. Ballester-Bolinches J. C. Beidleman John Cossey R. Esteban-Romero M. F. Ragland Jack Schmidt 《Archiv der Mathematik》2009,92(6):549-557
The aim of this paper is to prove certain characterization theorems for groups in which permutability is a transitive relation,
the so called -groups. In particular, it is shown that the finite solvable -groups, the finite solvable groups in which every subnormal subgroup of defect two is permutable, the finite solvable groups
in which every normal subgroup is permutable sensitive, and the finite solvable groups in which conjugate-permutability and
permutability coincide are all one and the same class. This follows from our main result which says that the finite modular
p-groups, p a prime, are those p-groups in which every subnormal subgroup of defect two is permutable or, equivalently, in which every normal subgroup is
permutable sensitive. However, there exist finite insolvable groups which are not -groups but all subnormal subgroups of defect two are permutable.
Received: 13 August 2008 相似文献
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D. Nemzer 《Integral Transforms and Special Functions》2016,27(8):653-666
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Zvonimir Janko 《Mathematische Zeitschrift》2008,258(3):629-635
We determine here up to isomorphism the structure of any finite nonabelian 2-group G in which every two distinct maximal abelian subgroups have cyclic intersection. We obtain five infinite classes of such 2-groups
(Theorem 1.1). This solves for p = 2 the problem Nr. 521 stated by Berkovich (in preparation). The more general problem Nr. 258 stated by Berkovich (in preparation)
about the structure of finite nonabelian p-groups G such that A ∩ B = Z(G) for every two distinct maximal abelian subgroups A and B is treated in Theorems 3.1 and 3.2. In Corollary 3.3 we get a new result for an arbitrary finite 2-group. As an application
of Theorems 3.1 and 3.2, we solve for p = 2 a problem of Heineken-Mann (Problem Nr. 169 stated in Berkovich, in preparation), classifying finite 2-groups G such that A/Z(G) is cyclic for each maximal abelian subgroup A (Theorem 4.1).
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Maria De Falco Francesco de Giovanni 《Bulletin of the Brazilian Mathematical Society》2000,31(1):73-80
A group is said to be aT-group if all its subnormal subgroups are normal. The structure of groups satisfying the minimal condition on subgroups that do not have the propertyT is investigated. Moreover, locally soluble groups with finitely many conjugacy classes of subgroups which are notT-groups are characterized. 相似文献
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Let H be a subgroup of a finite group G, and assume that p is a prime that does not divide |G : H|. In favorable circumstances, one can use transfer theory to deduce that the largest abelian p-groups that occur as factor groups of G and of H are isomorphic. When this happens, Tate’s theorem guarantees that the largest not-necessarily-abelian p-groups that occur as factor groups of G and H are isomorphic. Known proofs of Tate’s theorem involve cohomology or character theory, but in this paper, a new elementary
proof is given. It is also shown that the largest abelian p-factor group of G is always isomorphic to a direct factor of the largest abelian p-factor group of H.
Received: 17 June 2008 相似文献
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