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Normalp-subgroups in the group of outer automorphisms of a finitep-group

โœ Scribed by Peter Schmid


Publisher
Springer-Verlag
Year
1976
Tongue
French
Weight
403 KB
Volume
147
Category
Article
ISSN
0025-5874

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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