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A non-LEA sofic group

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Abstract

We describe elementary examples of finitely presented sofic groups which are not residually amenable (and thus not initially subamenable or LEA, for short). We ask if an amalgam of two amenable groups over a finite subgroup is residually amenable and answer this positively for some special cases, including countable locally finite groups, residually nilpotent groups and others.

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Acknowledgements

The authors would like to thank the referee for pointing out the validity of the second sentence of Theorem 1 and for many suggestions which improved the presentation.

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Authors and Affiliations

  1. Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    ADITI KAR

  2. University of Oxford, Oxford, OX2 6GG, UK

    NIKOLAY NIKOLOV

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  1. ADITI KAR
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  2. NIKOLAY NIKOLOV
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Correspondence to NIKOLAY NIKOLOV.

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Communicating Editor: B Sury

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KAR, A., NIKOLOV, N. A non-LEA sofic group. Proc Math Sci 127, 289–293 (2017). https://doi.org/10.1007/s12044-016-0315-2

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  • DOI: https://doi.org/10.1007/s12044-016-0315-2

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