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A -group with positive rank gradient
-
Jan-Christoph Schlage-Puchta
Published/Copyright:
March 6, 2012
Abstract.
We construct, for 
and 
,
a 
-generated 
-group 
which, in an asymptotic sense,
behaves almost like a 
-generated free pro-
-group. We show
that a subgroup of index 
needs 
generators, and
that the subgroup growth of 
satisfies
, where 
is the
-generated free pro-
-group. To do this we introduce a new
invariant for finitely-generated groups and study some of its basic
properties.
Received: 2011-02-15
Published Online: 2012-03-06
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Lower signalizer lattices in alternating and symmetric groups
- Group rings in which the group of units is hyperbolic
- The normalizer property for integral group rings of finite solvable T-groups
- Finite -groups all of whose proper subgroups have cyclic Frattini subgroups
- A -group with positive rank gradient
- New criteria for equivalence of locally compact abelian groups
- Rough ends of infinite primitive permutation groups
- Automorphism groups of rooted trees have property (FA): A new proof
- About the metric approximation of Higman's group
