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

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
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### References:

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