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Most finitely generated subgroups of infinite unitriangular matrices are free

Published online by Cambridge University Press:  17 April 2009

Waldemar Hołubowski
Waldemar Hołubowski
Affiliation:
Institute of Mathematics, Silesian Technical University, Kaszubska 23, 44–101 Gliwice, Poland e-mail: [email protected]
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In this note we prove that the group G of infinite dimensional upper unitriangular matrices over a finite field contains an explicit countable subgroup ‘full’ of free subgroups. We deduce from this fact that, in a suitable sense, almost all k–generator subgroups of G are free groups of rank k.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 419 - 423
Copyright
Copyright © Australian Mathematical Society 2002

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