Deficiency and commensurators-Reference-Cited by-同舟云学术

Deficiency and commensurators

Published:2018-01-20 Issue:3 Volume:21 Page:511-530
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Hillman Jonathan A.¹

Affiliation:

1. School of Mathematics and Statistics , University of Sydney , Sydney , NSW 2006 , Australia

Abstract

Abstract We show that if π is the fundamental group of a 4-dimensional infrasolvmanifold then - 2 ≤ def ⁢ ( π ) ≤ 0

{-2\leq\mathrm{def}(\pi)\leq 0}

, and give examples realizing each value allowed by our constraints, for each possible value of the rank of π / π ′

{\pi/\pi^{\prime}}

. We also consider the abstract commensurators of such groups. Finally, we show that if G is a finitely generated group, the kernel of the natural homomorphism from G to its abstract commensurator Comm ⁢ ( G )

{\mathrm{Comm}(G)}

is locally nilpotent by locally finite, and is finite if def ⁢ ( G ) > 1

{\mathrm{def}(G)>1}

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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