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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
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Norms over finitely generated Abelian group [PDF]
International Journal of Algebra, 2019 In this research article, norms are studied for group structures in terms of left and right invariant metrics, as well as some useful results are negotiated.
Muhammad Sarfraz, Yongjin Li
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Bigenetic properties of finitely generated hyper- (Abelian-by-finite) groups [PDF]
Journal of the Australian Mathematical Society, 1973 Let be a class and p a property of groups. We say that p is a bigenetic property of p-groups (or more simply, p is bigenetic in p-groups) if an p-group G has the property p whenever all two-generator subgroups of G have p.
J. Lennox
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A Proof of the Basis Theorem for Finitely Generated Abelian Groups [PDF]
Journal of the London Mathematical Society, 1951 R. Rado
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Automorphism Classes of Elements in Finitely Generated Abelian Groups
, 2011 We will show that every element of a finitely generated abelian group is automorphically equivalent what we will define to be a {\em representative element} in a {\em repeat-free subgroup}, and for finite abelian groups we can count the number of automorphism classes of elements.
Charles F. Rocca
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Tensor powers of modules over finitely generated abelian groups
Journal of Algebra, 1985 In an earlier paper [ 11, the authors investigated, as a major component of their final result, a special case of the following question. Let R be a commutative ring with unity, G a finitely generated abelian group and A4 a finitely generated RG-module. Consider the tensor power @“, M as an RG-module via the diagonal action of G.
Robert Bieri, J. R. J. Groves
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The Complement of a Finitely Generated Direct Summand of an Abelian Group [PDF]
Proceedings of the American Mathematical Society, 1956 P. Cohn
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Fields with Finitely Generated Abelian Automorphism Groups
Bulletin of the Faculty of Science, Ibaraki University. Series A, Mathematics, 1969 Ryûki Matsuda, Shinkichi Hirabuki
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Measurable Tilings by Abelian Group Actions [PDF]
International mathematics research notices, 2022 Let $X$ be a measure space with a measure-preserving action $(g,x) \mapsto g \cdot x$ of an abelian group $G$. We consider the problem of understanding the structure of measurable tilings $F \odot A = X$ of $X$ by a measurable tile $A \subset X ...
Jan Greb'ik +3 more
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