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On locally nilpotent groups

Published online by Cambridge University Press:  24 October 2008

D. H. McLain  and
P. Hall
D. H. McLain
Affiliation:
PeterhouseCambridge
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Extract

1. If P is any property of groups, then we say that a group G is ‘locally P’ if every finitely generated subgroup of G satisfies P. In this paper we shall be chiefly concerned with the case when P is the property of being nilpotent, and will examine some properties of nilpotent groups which also hold for locally nilpotent groups. Examples of locally nilpotent groups are the locally finite p-groups (groups such that every finite subset is contained in a finite group of order a power of the prime p); indeed, every periodic locally nilpotent group is the direct product of locally finite p-groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 5 - 11
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

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