Decomposing locally compact groups into simple pieces

2008/11/30 by Pierre-Emmanuel Caprace, Nicolas Monod · 2 citations
Mathematics · #math.GR #math.MG

paper · pdf · doi:10.1017/s0305004110000368

published as Math. Proc. Cambridge Philos. Soc. 150 (2011), 97--128 · Index added; minor changes

arxiv created 2010/05/05 · arxiv updated 2012/07/10

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.

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