Results 11 to 20 of about 2,666 (229)
Groups with many abelian subgroups
Journal of Algebra, 2011 The authors classify all groups all of whose subgroups of infinite index are Abelian. This class of groups is closed with respect to subgroups and quotient groups (but not a formation). Main theorem: If \(G\) is a non-Abelian group as defined, then \(G\) is finitely generated and \textit{either} (a) \(G/Z(G)\) is a just-infinite group with no Abelian ...
DE FALCO, MARIA +3 more
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G-Groups and Biuniform Abelian Normal Subgroups [PDF]
Advances in Group Theory and Applications, 2016 We prove a weak form of the Krull-Schmidt Theorem concerning the behavior of direct-product decompositions of $G$-groups, biuniform abelian $G$-groups, $G$-semidirect products and the $G$-set $Hom(H,A)$. Here $G$ and $A$ are groups and $H$ is a $G$-group.
María José Arroyo Paniagua +1 more
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Balanced subgroups of abelian groups [PDF]
Transactions of the American Mathematical Society, 1975 The balanced subgroups of Fuchs are generalised to arbitrary abelian groups. Projectives and injectives with respect to general balanced exact sequences are classified; a new class of groups is introduced in order to classify these projectives.
Roger H. Hunter
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Embedding of Abelian Subgroups in p-Groups [PDF]
Transactions of the American Mathematical Society, 1971 Research concerning the embedding of abelian subgroups in p p -groups generally has proceeded in two directions; either considering abelian subgroups of small index (cf. J. L. Alperin, Large abelian subrgoups of p p -groups, Trans. Amer. Math. Soc. 117 (1965), 10-20) or considering elementary abelian subgroups of small
Marc W. Konvisser
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Factorizing profinite groups into two Abelian subgroups [PDF]
International Journal of Group Theory, 2013 We prove that the class of profinite groups $G$ that have a factorization $G=AB$with $A$ and $B$ abelian closed subgroups, is closed under taking strict projective limits.This is a generalization of a recent result by K.H.~Hofmann and F.G.~Russo.As an ...
Wolfgang Herfort
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Groups with Finitely Many Isomorphism Classes of Non-Normal Subgroups [PDF]
Advances in Group Theory and Applications, 2020 We study groups in which the non-normal subgroups fall into finitely many isomorphism classes. We prove that a locally generalized radical group with this property is abelian-by-finite and minimax.
Leonid A. Kurdachenko +2 more
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Subgroup transitivity in abelian groups [PDF]
Proceedings of the American Mathematical Society, 1998 We generalize an appropriate modification of the classical notion of transitivity in abelian p p -groups from one that is ...
Hill, Paul, Kirchner West, Jane
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Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group [PDF]
Mathematics Interdisciplinary Research, 2020 Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this
Zahra Garibbolooki, Sayyed Heidar Jafari
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On T-Characterized Subgroups of Compact Abelian Groups
Axioms, 2015 A sequence \(\{ u_n \}_{n\in \omega}\) in abstract additively-written Abelian group \(G\) is called a \(T\)-sequence if there is a Hausdorff group topology on \(G\) relative to which \(\lim_n u_n =0\).
Saak Gabriyelyan
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n-capability of A-groups [PDF]
Mathematics Interdisciplinary Research, 2020 Following P. Hall a soluble group whose Sylow subgroups are all abelian is called A-group. The purpose of this article is to give a new and shorter proof for a criterion on the capability of A-groups of order p2q, where p and q are distinct primes ...
Marzieh Chakaneh +2 more
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