Abstract
We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series – i.e. a finite normal series in which each factor is either compact, discrete, or a topological chief factor. A Jordan–Hölder theorem additionally holds for the ‘large’ factors in an essentially chief series.
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Acknowledgements
Many of the ideas for this project were developed during a stay at the Mathematisches Forschungsinstitut Oberwolfach; we thank the institute for its hospitality. We also thank the anonymous referees for their detailed suggestions.
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Communicated by Andreas Thom.
Colin D. Reid is an ARC DECRA fellow. Research supported in part by ARC Discovery Project DP120100996.
Phillip R. Wesolek was supported by ERC Grant #278469.
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Reid, C.D., Wesolek, P.R. The essentially chief series of a compactly generated locally compact group. Math. Ann. 370, 841–861 (2018). https://doi.org/10.1007/s00208-017-1597-0
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DOI: https://doi.org/10.1007/s00208-017-1597-0