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The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups

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Abstract

The scale of an endomorphism, \(\alpha \), of a totally disconnected, locally compact group \(G\) is the minimum index \([\alpha (U) : \alpha (U)\cap U]\), for \(U\) a compact, open subgroup of \(G\). A structural characterization of subgroups at which the minimum is attained is established. This characterization extends the notion of subgroup tidy for \(\alpha \) from the previously understood case when \(\alpha \) is an automorphism to the case when \(\alpha \) is merely an endomorphism.

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Acknowledgments

This research is supported by the Australian Research Council Discovery Grant DP0984342. I am grateful to the referee for carefully reading the first version of the paper and making many thoughtful corrections and suggestions. Several errors highlighted by the referee have been corrected and numerous suggestions regarding wording and notation that have improved the exposition significantly have been followed.

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  1. The University of Newcastle, University Drive, Callaghan, 2308, Australia

    George A. Willis

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  1. George A. Willis
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Correspondence to George A. Willis.

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Willis, G.A. The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups. Math. Ann. 361, 403–442 (2015). https://doi.org/10.1007/s00208-014-1074-y

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  • DOI: https://doi.org/10.1007/s00208-014-1074-y

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