The group of outer automorphisms of an infinite nilpotent p-group and its normal p-subgroups. (Italian) Zbl 0588.20027

Marconi, Riccardo

Rend. Sem. Mat. Univ. Padova 74, 123-127 (1985).

This paper is a contribution to the literature on normal p-subgroups of the automorphism groups of p-groups. The finite case was dealt with by Peter Schmid. Here it is shown that if G is an infinite nilpotent p-group and Out G has no non-identity normal p-subgroup, then there are three possibilities. (1) G is elementary Abelian. (2) G is divisible and p is odd. (3) G is the central product of P and C, where P is a finite extraspecial group of exponent \(p\neq 2\) and C is a quasicyclic p-group. The proof owes some details to a paper of Menegazzo and Stonehewer.

Reviewer: N.Blackburn

MSC:

20F28	Automorphism groups of groups
20F18	Nilpotent groups
20F50	Periodic groups; locally finite groups
20E07	Subgroup theorems; subgroup growth
20E36	Automorphisms of infinite groups

Keywords:

normal p-subgroups; automorphism groups of p-groups; infinite nilpotent p-group; extraspecial group

References:

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