Proceedings - Mathematical Sciences

, Volume 127, Issue 2, pp 289–293 | Cite as

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.

Keywords

Amenable LEF LEA sofic group. 

2010 Mathematics Subject Classification.

20E08 20E26. 
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Notes

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.

References

  1. [1]
    Bekka B, de la Harpe P and Valette A, Kazhdan’s property (T), New Math. Monogr. 11 CUP (2008)Google Scholar
  2. [2]
    Berlai F, Residual properties of free products, arXiv:1405.0244
  3. [3]
    Capraro V and Lupini M, Introduction to Sofic and hyperlinear groups and Connes’ embedding conjecture, arXiv:1309.2034
  4. [4]
    Collins B and Dykema K J, Free products of sofic groups with amalgamation over monotileably amenable groups, Münster. J. Math. 4 (2011) 101–117MathSciNetMATHGoogle Scholar
  5. [5]
    Cornulier Y, A sofic group away from amenable groups, Math. Ann. 350 (2) (2011) 269–275MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Elek G and Szabo E, Sofic representations of amenable groups, Proc. Amer. Math. Soc. 139 (12) (2011) 4285–4291MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    Eymard P, Moyennes invariantes et representations unitaires, Lecture Notes in Mathematics 300 (1972) (Berlin: Springer-Verlag)CrossRefMATHGoogle Scholar
  8. [8]
    Glasner Y and Monod N, Amenable action, free products and a fixed point property, Bull. Lond. Math. Soc. 39 (1) (2007) 138–150MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Gromov M, Endomorphisms of symbolic algebraic varieties, J. European Math. Soc. 1 (2) (1999) 109–197MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    Paunescu L, On sofic actions and equivalence relations, J. Funct. Anal. 261 (9) (2011) 2461–2485MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Scott P and Wall T, Topological methods in group theory, homological group theory, LMS Lecture Notes Series 36. CUP (1979)Google Scholar
  12. [12]
    Serre J P, Trees, Springer Monographs in Mathematics (2003)Google Scholar

Copyright information

© Indian Academy of Sciences 2016

Authors and Affiliations

  1. 1.Royal HollowayUniversity of LondonEghamUK
  2. 2.University of OxfordOxfordUK

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