Decomposing locally compact groups into simple pieces

We present a contribution to the structure theory of locally compact groups. The emphasis is put 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 complete description of groups all of whose proper quotients are compact, of characteristically simple groups and of groups admitting a subnormal series with all subquotients compact, or compactly generated Abelian, or compactly generated and topologically simple. Two appendices introduce results and examples around the concept of quasi-product.


Published in:
Math. Proc. Cambridge Philos. Soc., 150, 97--128
Year:
2011
Keywords:
Laboratories:




 Record created 2008-10-29, last modified 2018-03-17


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