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2008•Mathematica SlovacaOpen access

On automorphisms of finite Abelian p-groups

Marek Golasiński, Daciberg Lima Gonçalves

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Abstract

Abstract Let 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.

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Abstract Let 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.

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Available abstract

Abstract Let 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.

Key concepts: Mathematics, Automorphism, Abelian group, Rank of an abelian group, Elementary abelian group, Automorphism group, Outer automorphism group, Inner automorphism

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