The small index property for free nilpotent groups

Details The small index property for free nilpotent groups The small index property for free nilpotent groups

2011-11-23

arxiv.org/abs/1111.5635v2

Mathematics

Group Theory

18 pp

Scientific paper

Let F be a relatively free algebra of infinite rank. We say that F has the SMALL INDEX PROPERTY if any subgroup of Gamma=Aut(F) of index at most rank(F) contains the pointwise stabilizer Gamma_(U) of a subset U of F of cardinality less than rank(F). We prove that every infinitely generated free nilpotent/abelian group has the small index property, and discuss a number of applications.

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