On automorphisms of finite Abelian <Emphasis Type="Italic">p</Emphasis>-groups |
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Authors: | Marek Golasiński Daciberg Lima Gonçalves |
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Institution: | 1.Faculty of Mathematics and Computer Science,Nicolaus Copernicus University,Toruń,Poland;2.Department of Mathematics-IME,University of S?o Paulo,Cidade de S?o Paulo,Brasil |
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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.
This work has begin during the visit of the second author to the Faculty of Mathematics and Computer Science, Nicolaus Copernicus
University during the period July 31–August 13, 2005. This visit was supported by the Nicolaus Copernicus University and a
grant from Cnpq. |
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Keywords: | finite abelian p-group automorphism group semi-direct product |
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