Decomposing locally compact groups into simple pieces

By P. Caprace, Nicolas Monod. Mathematical Proceedings of the Cambridge Philosophical Society, 2008

110 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6d121694db07e5a341aae82df51bac9397d1adc1

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In Geometry and Topology

1. P. Caprace
2. Colin D. Reid
3. George A. Willis
4. Phillip R. Wesolek
5. Nicolas Monod
6. Tom De Medts
7. Denis V. Osin
8. K. Fujiwara

In Mathematical Physics

1. P. Caprace
2. Phillip R. Wesolek
3. George A. Willis
4. Colin D. Reid
5. Nicolas Monod
6. Denis V. Osin
7. K. Fujiwara
8. A. Iozzi

Citations in the corpus

• Isometry groups of non‐positively curved spaces: discrete subgroups (2009, background): “) The proofs will use the following fact established in [28].”
• Isometry groups of non‐positively curved spaces: structure theory (2008, background): “A variant of this proposition is proved in [26]; since the proof is short, we give it for the sake of completeness.”
• LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS (2014, methodology): “At this point, let us merely mention the following observation, inspired by [17].”
• Simple locally compact groups acting on trees and their germs of automorphisms (2010, background): “It was moreover shown in [ CM11 ] that, under some natural restrictions which exclude the existence of innite discrete quotients, a compactly generated locally compact group decomposes into nitely many pieces (namely subquotients) which are all compact, or compactly generated abelian, or compactly g”
• Elementary totally disconnected locally compact groups (2014, background): “Proposition 2.5 (Caprace and Monod [7, Proposition 2.5]).”