Results 21 to 30 of about 52,191 (255)
Solitary subgroups of Abelian groups
Expositiones Mathematicae, 2021 A subgroup \(K\) of an abelian group \(G\) is called solitary if \(G\) contains no other subgroup isomorphic to \(K\). The paper is dedicated to the study of solitary subgroups for some important classes of abelian groups. Complete descriptions are presented in Theorem 3 and Theorem 4.
Călugăreanu, Grigore +1 more
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On the Classification Problem for Rank 2 Torsion-Free Abelian Groups [PDF]
, 2000 We study here some foundational aspects of the classification problem for torsion-free abelian groups of finite rank. These are, up to isomorphism, the subgroups of the additive groups (Q^n, +), for some n = 1, 2, 3,....
Kechris, Alexander S.
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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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On the number of subgroups of a given exponent in a finite abelian group [PDF]
, 2017 This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups.
Tóth, László, Tărnăuceanu, Marius
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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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Normality in Uncountable Groups [PDF]
Advances in Group Theory and Applications, 2017 The main purpose of this paper is to describe the structure of uncountable groups of cardinality $\aleph$ in which all subgroups of cardinality $\aleph$ are normal.
Maria De Falco +3 more
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Dimensional groups and fields [PDF]
, 2019 We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that pseudofinite groups
Wagner, Frank Olaf
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Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem [PDF]
, 2001 In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups, finding hidden
Ivanyos, Gabor +2 more
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Some definition of the Artin exponent of finite groups [PDF]
, 1996 The Artin exponent induced from cyclic subgroups of finite groups was studied extensively by T.Y. Lam. A Burnside ring theoretic version of Lam's results for $p$-groups was given by the author in an earlier paper.
Nwabueze, K. K.
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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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