Abstract: 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.
Publication Year: 1956
Publication Date: 1956-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 39
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