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 โธ l Fix p n G, where โธ is the unique maximal normal p-subgroup of
โฆ LIBER โฆ
Normalp-subgroups in the group of outer automorphisms of a finitep-group
โ Scribed by Peter Schmid
- Publisher
- Springer-Verlag
- Year
- 1976
- Tongue
- French
- Weight
- 403 KB
- Volume
- 147
- Category
- Article
- ISSN
- 0025-5874
No coin nor oath required. For personal study only.
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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