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Abstract
We prove that a finitely generated soluble residually finite group has polynomial index growth if and only if it is a minimax group. We also show that if a finitely generated group with PIG is residually finite-soluble then it is a linear group. These results apply in particular to boundedly generated groups; they imply that every infinite BG residually finite group has an infinite linear quotient.
Received: 2005-05-11
Accepted: 2006-10-12
Published Online: 2008-03-04
Published in Print: 2007-11-01
© Walter de Gruyter
