Results 21 to 30 of about 11,420 (266)
Thickness of the subgroup intersection graph of a finite group
AIMS Mathematics, 2021 Let $ G $ be a finite group. The intersection graph of subgroups of $ G $ is a graph whose vertices are all non-trivial subgroups of $ G $ and in which two distinct vertices $ H $ and $ K $ are adjacent if and only if $ H\cap K\neq 1 $. In this paper, we
Huadong Su, Ling Zhu
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Abelian Subgroups of Garside Groups [PDF]
Communications in Algebra, 2008 In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for ...
Lee, Eon-Kyung, Lee, Sang Jin
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Normalizers and centralizers of subgroups in non-Abelian groups of small order [PDF]
Компьютерные исследования и моделирование, 2012 By applying the computer program, which is created by authors, we obtain the exact representation of normalizers and centralizers of all nontrivial subgroups in non-Abelian groups G under the condition |G|20.
Ilya Anatolievih Shilin +1 more
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Influence of complemented subgroups on the structure of finite groups [PDF]
International Journal of Group Theory, 2021 P. Hall proved that a finite group $G$ is supersoluble with elementary abelian Sylow subgroups if and only if every subgroup of $G$ is complemented in $G$. He called such groups complemented. A. Ballester-Bolinches and X.
Izabela Malinowska
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THE NUMBER OF CYCLIC SUBGROUPS OF FINITE ABELIAN GROUPS AND MENON’S IDENTITY [PDF]
Bulletin of the Australian Mathematical Society, 2018 We give a new formula for the number of cyclic subgroups of a finite abelian group. This is based on Burnside’s lemma applied to the action of the power automorphism group. The resulting formula generalises Menon’s identity.
M. Tărnăuceanu
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Isolated subgroups of finite abelian groups [PDF]
Czechoslovak Mathematical Journal, 2022 We say that a subgroup $H$ is isolated in a group $G$ if for every $x\in G$ we have either $x\in H$ or $\langle x\rangle\cap H=1$. In this short note, we describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite
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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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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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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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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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