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The automorphism group of an abelian p-group and its noncentral normal subgroups

โœ Scribed by Jutta Hausen

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
582 KB
Volume
30
Category
Article
ISSN
0021-8693

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We will show that for any integer n G 0, the automorphism group of an abelian p-group G, p G 3, contains a unique subgroup which is maximal with respect to being normal and having exponent less than or equal to p n . This subgroup is โŒธ l Fix p n G, where โŒธ is the unique maximal normal p-subgroup of

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Let F be a free group of rank n. Denote by Out F its outer automorphism n n group, that is, its automorphism group modulo its inner automorphism group. For arbitrary n, by considering group actions on finite connected graphs, we derived the maximum order of finite abelian subgroups in Out F . Moreov