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Decomposing locally compact groups into simple pieces

Published online by Cambridge University Press:  02 September 2010

PIERRE-EMMANUEL CAPRACE  and
NICOLAS MONOD
PIERRE-EMMANUEL CAPRACE
Affiliation:
UCLouvain, 1348 Louvain-la-Neuve, Belgium. e-mail: pe.caprace@uclouvain.be
NICOLAS MONOD
Affiliation:
EPFL, 1015 Lausanne, Switzerland. e-mail: nicolas.monod@epfl.ch
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Abstract

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic cocompact subgroup which is either connected or admits a non-compact non-discrete topologically simple quotient. We also provide a description of characteristically simple groups and of groups all of whose proper quotients are compact. We show that Noetherian locally compact groups without infinite discrete quotient admit a subnormal series with all subquotients compact, compactly generated Abelian, or compactly generated topologically simple.

Two appendices introduce results and examples around the concept of quasi-product.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 1 , January 2011 , pp. 97 - 128
Copyright
Copyright © Cambridge Philosophical Society 2010

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