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Bulletin of the London Mathematical Society Advance Access originally published online on April 17, 2009
Bulletin of the London Mathematical Society 2009 41(4):599-612; doi:10.1112/blms/bdp032
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© 2009 London Mathematical Society

Linear groups with many two-generator soluble subgroups

John S. Wilson

University College
Oxford
OX1 4BH
United Kingdom

Received 21 May 2008.

Let G be a linear group of degree n over a field and let S be any generating set. It is proved that (a) if every pair of products of at most Formula elements of S {cup} S– 1 generates a soluble group then G is soluble and (b) if G is soluble and every pair of products of at most Formula elements of S {cup} S–1 generates a nilpotent group then G is locally nilpotent.

2000 Mathematics Subject Classification 20F16, 20H20.


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