On groups that are residually of finite rank
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Letr be a fixed positive integer. A groupG has (Prüfer) rankr if every finitely generated subgroup ofG can be generated byr elements andr is the least such integer. In this paper we consider groups that are residually of rankr. Among other things we prove that a periodic group that is residually (of rankr and locally finite) is locally finite and obtain the structure of groups that are residually (of rankr and locally soluble). A number of examples are also given to illustrate the limitations of these theorems.
KeywordsNormal Subgroup Finite Group Nilpotent Group Finite Index Finite Rank
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