On automorphisms of finite Abelianp-groups

✍ Scribed by Marek Golasiński; Daciberg Lima Gonçalves

• Book ID: 111492969
• Publisher: SP Versita
• Year: 2008
• Tongue: English
• Weight: 169 KB
• Volume: 58
• Category: Article
• ISSN: 0139-9918
• DOI: 10.2478/s12175-008-0084-1

✦ Synopsis

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.