The Small Index Property for Free Nilpotent Groups |
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| Authors: | Vladimir Tolstykh |
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| Institution: | 1. Department of Mathematics and Computer Science , Istanbul Arel University , Istanbul , Turkey vladimirtolstykh@arel.edu.tr |
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| Abstract: | Let F be a relatively free algebra of infinite rank ?. We say that F has the small index property if any subgroup of Γ = Aut(F) of index at most ? contains the pointwise stabilizer Γ(U) of a subset U of F of cardinality less than ?. 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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| Keywords: | Automorphisms Nilpotent groups Small index property |
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