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- W2023987341 abstract "It is well known [2; Theorem 12.2.21 that if G is a finite p-group with Frattini subgroup @, then the group 5 of automorphisms of G fixing G/Q elementwise is a finite p-group and therefore nilpotent. In this paper we shall obtain an upper bound for the nilpotency class of 3 (Theorem 3). This is done by relating a certain central series of G to a central series of 5. The argument uses induction (Theorem 2 giving information about the center of 3) and depends on a partly well-known general result (Theorem 1 and Corollary 1) showing how certain subgroups of a group lead to normal subgroups of its group of automorphisms. We conclude by applying the theory to Abelian p-groups, wreath products, etc." @default.
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- W2023987341 date "1966-11-01" @default.
- W2023987341 modified "2023-10-16" @default.
- W2023987341 title "The automorphism group of finite p-groups" @default.
- W2023987341 cites W4312893838 @default.
- W2023987341 doi "https://doi.org/10.1016/0021-8693(66)90032-9" @default.
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