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G. Cutolo and H. Smith
Residually finite subgroups of some countable McLain groups
Arch. Math. (Basel), 93, (2009), pp. 513–520.
doi: 10.1007/s00013-009-0061-0
MathSciNet Zentralblatt Abstract Full Text
Abstract
The McLain groups are groups of finitary linear transformations that, besides being of considerable interest in their own right, constitute a most useful source of counterexamples to conjectures arising in the investigation of locally nilpotent groups. In this article it is shown that certain torsion-free McLain groups have subgroups “of periodic index” that are residually finite. This has a bearing on the question as to which McLain groups might embed in simple locally soluble-by-finite groups.
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