scholarly journals The Automorphism Group of Non-Abelian Group of Order p^4

2020 ◽  
Vol 5 (2) ◽  
pp. 197-204
Author(s):  
Reza Orfi ◽  
Keyword(s):  
Abelian Group ◽  
Automorphism Group

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

The automorphism group of a finitely generated virtually abelian group

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Bettina Eick
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Automorphism Groups ◽  
Finitely Generated ◽  
Crystallographic Groups ◽  
Practical Algorithm

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.

scholarly journals Dynamics of Endomorphism of Finite Abelian Groups

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Zhao Jinxing ◽  
Nan Jizhu
Keyword(s):  
Fixed Point ◽  
Abelian Group ◽  
Dynamical Systems ◽  
Automorphism Group ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Point System ◽  
Finite Abelian Groups

We study the dynamics of endomorphisms on a finite abelian group. We obtain the automorphism group for these dynamical systems. We also give criteria and algorithms to determine whether it is a fixed point system.

scholarly journals On automorphisms of finite Abelian p-groups

2008 ◽  
Vol 58 (4) ◽  
Author(s):  
Marek Golasiński ◽  
Daciberg Gonçalves
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finitely Generated ◽  
Type K ◽  
Group A ◽  
Necessary And Sufficient ◽  
Torsion Part

AbstractLet A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A p.For a finite abelian p-group A of type (k 1, ..., k n), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k 1, k 2) is analyzed.

Representations of holomorphs of group extensions with Abelian kernels

1975 ◽  
Vol 78 (3) ◽  
pp. 357-368 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Finite Rank ◽  
Automorphism Groups ◽  
Abelian Groups ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Soluble Groups ◽  
Group Extensions

This paper is devoted to the construction of faithful representations of the automorphism group and the holomorph of an extension of an abelian group by some other group, the representations here being homomorphisms into certain restricted parts of the automorphism groups of smallish abelian groups. We apply these to two very specific cases, namely to finitely generated metabelian groups and to certain soluble groups of finite rank. We describe the applications first.

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