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A Finite Index Property of Certain Solvable Groups

Published online by Cambridge University Press:  20 November 2018

A. H. Rhemtulla  and
H. Smith
A. H. Rhemtulla
Affiliation:
University of Alberta, Edmonton, Canada T6G 2G1
H. Smith
Affiliation:
York University, Downsview, Canada M3J 1P3
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Abstract

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A group G is said to have the FINITE INDEX property (G is an FI-group) if, whenever H≤G, xp ∈ H for some x in G and p > 0, then |〈H, x〉: H| is finite. Following a brief discussion of some locally nilpotent groups with this property, it is shown that torsion-free solvable groups of finite rank which have the isolator property are FI-groups. It is deduced from this that a finitely generated torsion-free solvable group has an FI-subgroup of finite index if and only if it has finite rank.

Keywords

20E3420F16
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 485 - 489
Copyright
Copyright © Canadian Mathematical Society 1984

Footnotes

1

Research partially supported by a grant from Natural Sciences and Engineering Research Council of Canada.

References

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