English

Expansion in $SL_d(O_K/I)$, $I$ square-free

Group Theory 2012-05-15 v1

Abstract

Let S be a fixed symmetric finite subset of SL_d(O_K) that generates a Zariski dense subgroup of SL_d(O_K) when we consider it as an algebraic group over Q by restriction of scalars. We prove that the Cayley graphs of SL_d(O_K/I) with respect to the projections of S is an expander family if I ranges over square-free ideals of O_K if d=2 and K is an arbitrary numberfield, or if d=3 and K=Q.

Keywords

Cite

@article{arxiv.1001.3664,
  title  = {Expansion in $SL_d(O_K/I)$, $I$ square-free},
  author = {Péter P. Varjú},
  journal= {arXiv preprint arXiv:1001.3664},
  year   = {2012}
}