Expanders , Rank and Graphs of Groups

@inproceedings{Lackenby2008ExpandersR,
  title={Expanders , Rank and Graphs of Groups},
  author={Marc Lackenby},
  year={2008}
}
A central principle of this paper is that, for a finitely presented group G, the algebraic properties of its finite index subgroups should be reflected by the geometry of its finite quotients. These quotients can indeed be viewed as geometric objects, in the following way. If we pick a finite set of generators for G, these map to a generating set for any finite quotient and hence endow this quotient with a word metric. This metric of course depends on the choice of generators, but if we were to… CONTINUE READING
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References

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Showing 1-10 of 16 references

Discrete Groups, Expanding Graphs and Invariant Measures

  • A. Lubotzky
  • Progr. in Math
  • 1994
Highly Influential
4 Excerpts

Groups and expanders, Expanding graphs (Princeton, 1992) 95–109, DIMACS Ser

  • A. Lubotzky, B. Weiss
  • Discrete Math. Theoret. Comput. Sci, 10, Amer…
  • 1993
Highly Influential
3 Excerpts

de la Harpe , Topics in Geometric Group Theory

  • R. Grigorchuk
  • Chicago Lect . Math
  • 2000

A . Lubotzky , Discrete Groups , Expanding Graphs and Invariant Measures

  • B. Weiss A. Lubotzky
  • Progr . in Math .
  • 1994

Venkataramana, Generators for all principal congruence subgroups of SL(n, Z) with n ≥ 3

  • T.N.B. Sury
  • Proc. Amer. Math. Soc
  • 1994
2 Excerpts

Groups and expanders , Expanding graphs ( Princeton , 1992 ) 95 – 109 , DIMACS Ser . Discrete Math . Theoret

  • P. Schupp R. Lyndon
  • Combinatorial group theory
  • 1993

Dimension function for discrete groups , Proceedings of Groups

  • A. Lubotzky
  • Andrews
  • 1986

Dimension function for discrete groups, Proceedings of Groups, St

  • A. Lubotzky
  • Andrews
  • 1985

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