Finitely generated groups with polynomial index growth

Details Finitely generated groups with polynomial index growth Finitely generated groups with polynomial index growth

2007-11-05

arxiv.org/abs/0711.0687v1

J. reine angew. Math. 612 (2007), 173-211

Mathematics

Group Theory

To appear in Crelle's Journal

Scientific paper

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.

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