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Outer automorphisms of hypercentral p-groups

Published online by Cambridge University Press:  18 May 2009

Orazio Puglisi
Orazio Puglisi
Affiliation:
Dipartimento di Matematica, Università di Trento, 1-38050 Povo-Italy, E-mail: puglisi@itnvax.science.unitn.it
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In his celebrated paper [3] Gaschiitz proved that any finite non-cyclic p-group always admits non-inner automorphisms of order a power of p. In particular this implies that, if G is a finite nilpotent group of order bigger than 2, then Out (G) = Aut(G)/Inn(G) =≠1. Here, as usual, we denote by Aut (G) the full group of automorphisms of G while Inn (G) stands for the group of inner automorphisms, that is automorphisms induced by conjugation by elements of G. After Gaschiitz proved this result, the following question was raised: “if G is an infinite nilpotent group, is it always true that Out (G)≠1?”

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 2 , May 1995 , pp. 243 - 247
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

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