Results 161 to 170 of about 34,296 (212)

Polynomial growth harmonic functions on finitely generated abelian groups [PDF]

Annals of Global Analysis and Geometry, 2011
In the present paper, we develop geometric analysis techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We provide a geometric analysis proof of the classical Heilbronn theorem (Heilbronn in
B. Hua, J. Jost, X. Li-Jost
semanticscholar   +5 more sources

The automorphism group of a finitely generated virtually abelian group

Groups Complexity Cryptology, 2016
AbstractWe describe a practical algorithm to compute the automorphism group of a finitely generated virtually abelian group. As application, we describe the automorphism groups of some small-dimensional crystallographic groups.
B. Eick
semanticscholar   +3 more sources

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On the product of finitely generated Abelian groups

Mathematical Notes of the Academy of Sciences of the USSR, 1973
It is shown that if a group G is a product of Abelian subgroups A and B one of which is finitely generated, then the group G will have a nontrivial normal subgroup that is contained either in A, or in B.
N. F. Sesekin
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Finitely Generated Abelian Groups

, 1988
A group is finitely generated if it has a finite set of generators. Finitely generated abelian groups may be classified. By this we mean we can draw up a list (albeit infinite) of “standard” examples, no two of which are isomorphic, so that if we are presented with an arbitrary finitely generated abelian group, it is isomorphic to one on our list.
M. A. Armstrong
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Quantifying lawlessness in finitely generated groups

Journal of group theroy, 2021
We introduce a quantitative notion of lawlessness for finitely generated groups, encoded by the lawlessness growth function A Γ : N → N \mathcal{A}_{\Gamma}\colon\mathbb{N}\to\mathbb{N} .
Henry Bradford
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On Commutator Length and Square Length of the Wreath Product of a Group by a Finitely Generated Abelian Group

, 2010
Let W = G ≀ H be the wreath product of G by an n-generator abelian group H. We prove that every element of W′ is a product of at most n+2 commutators, and every element of W2 is a product of at most 3n+4 squares in W. This generalizes our previous result.
M. Akhavan-Malayeri
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Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: A survey

, 2017
This is a self-contained introduction to the applications of ergodic theory of nonsingular (also known as quasi-invariant) group actions and the structure theorem for finitely generated abelian groups on the extreme values of stationary symmetric stable ...
Parthanil Roy
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Tame automorphisms of finitely generated abelian groups

Proceedings of the Edinburgh Mathematical Society, 1998
We characterize tame automorphisms of finitely generated abelian groups via a simple determinant condition.
Edward C. Turner, Daniel A. Voce
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TEST ELEMENTS IN FINITELY GENERATED ABELIAN GROUPS

International Journal of Algebra and Computation, 2002
We determine which finitely generated abelian groups have test elements and give examples when they exist.
Edward C. Turner, Charles F. Rocca
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Quantum Isometry group of dual of finitely generated discrete groups and quantum groups

, 2014
We study quantum isometry groups, denoted by $\mathbb{Q}(\Gamma, S)$, of spectral triples on $C^*_r(\Gamma)$ for a finitely generated discrete group coming from the word-length metric with respect to a symmetric generating set $S$.
Debashish Goswami, A. Mandal
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