Results 21 to 30 of about 472 (192)
A Proof of the Basis Theorem for Finitely Generated Abelian Groups [PDF]
Journal of the London Mathematical Society, 1951 R. Rado
openalex +4 more sources
Finite frattini factors in finitely generated Abelian-by-polycyclic groups [PDF]
Proceedings of the American Mathematical Society, 1973 A criterion for a group to be finite is used to prove that subgroups of finitely generated Abelian-by-polycyclic groups are finite if their Frattini factor groups are finite.
John C. Lennox
+5 more sources
Minimal additive complements in finitely generated abelian groups [PDF]
The Ramanujan Journal, 2021 Given two non-empty subsets $W,W'\subseteq G$ in an arbitrary abelian group $G$, $W'$ is said to be an additive complement to $W$ if $W + W'=G$ and it is minimal if no proper subset of $W'$ is a complement to $W$. The notion was introduced by Nathanson and previous work by him, Chen--Yang, Kiss--S ndor--Yang etc. focussed on $G =\mathbb{Z}$.
Arindam Biswas +3 more
openaire +6 more sources
The multiple holomorph of a finitely generated abelian group [PDF]
Journal of Algebra, 2017 W.H.~Mills has determined, for a finitely generated abelian group $G$, the regular subgroups $N \cong G$ of $S(G)$, the group of permutations on the set $G$, which have the same holomorph of $G$, that is, such that $N_{S(G)}(N) = N_{S(G)}( (G))$, where $ $ is the (right) regular representation.
Caranti, Andrea, F. Dalla Volta
openaire +3 more sources
On abelian subgroups of finitely generated metabelian groups [PDF]
Journal of Group Theory, 2013 Abstract.In this note we introduce the class ...
Vahagn H. Mikaelian +1 more
openalex +5 more sources
Finitely generic abelian lattice-ordered groups [PDF]
Transactions of the American Mathematical Society, 1983 The authors characterize the finitely generic abelian lattice-ordered groups and make application of this characterization to specific examples.
Dan Saracino, Carol Wood
openaire +1 more source
A residual property of finitely generated abelian-by-nilpotent groups
Journal of Algebra, 1974 Dan Segal
openalex +3 more sources
Fields with Finitely Generated Abelian Automorphism Groups
Bulletin of the Faculty of Science, Ibaraki University. Series A, Mathematics, 1969 Ryûki Matsuda, Shinkichi Hirabuki
openalex +4 more sources
Homological models for semidirect products of finitely generated Abelian groups [PDF]
Applicable Algebra in Engineering, Communication and Computing, 2012 Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the reduced bar construction of the group ring of G, B¯¯¯¯(ZZ[G]) , to a much smaller DGA-module hG. Such a contraction is called a homological model for G and is used as the input datum in
Víctor Álvarez +3 more
openalex +4 more sources
On structure analysis of finitely generated abelian groups
World Journal of Advanced Research and Reviews, 2022 In this paper we give an overview of the structural analysis of finitely generated abelian groups and modules. We give an overview of recent results on the structure theory of these objects in various situations, in particular in the case of torsionfree groups of infinite rank. We also mention several open problems.
openaire +2 more sources