Decomposing locally compact groups into simple pieces

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.

Index added; minor changes

References in corpus (3)

• Isometry groups of non-positively curved spaces: structure theory
• Abstract simplicity of complete Kac-Moody groups over finite fields
• Strange images of profinite groups

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