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Multiplicative Invariants and the Finite Co-Hopfian Property

Humphreys, JJAM; Johnson, FEA; (2009) Multiplicative Invariants and the Finite Co-Hopfian Property. Mathematika , 55 115 - 127. 10.1112/S0025579300000978. Green open access

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Abstract

A group is said to be, finitely co-Hopfian when it contains no proper subgroup of finite index isomorphic to itself. It is known that irreducible lattices in semisimple Lie groups are finitely co-Hopfian. However, it is not clear, and does not appear to be known, whether this property is preserved under direct product. We consider a strengthening of the finite co-Hopfian condition, namely the existence of a non-zero multiplicative invariant, and show that, under mild restrictions, this property is closed with respect to finite direct products. Since it is also closed with respect to commensurability, it follows that lattices in linear semisimple groups of general type are finitely co-Hopfian.

Type: Article
Title: Multiplicative Invariants and the Finite Co-Hopfian Property
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/S0025579300000978
Publisher version: http://dx.doi.org/10.1112/S0025579300000978
Language: English
Additional information: © 2009 Cambridge University Press
Keywords: Primary, 20E34, 20E99
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/80991
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