# Expansion in $SL dO K-I$, $I$ square-free - Mathematics > Group Theory

Expansion in $SL dO K-I$, $I$ square-free - Mathematics > Group Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: Let S be a fixed symmetric finite subset of SL dO K that generates aZariski dense subgroup of SL dO K when we consider it as an algebraic groupover Q by restriction of scalars. We prove that the Cayley graphs ofSL dO K-I with respect to the projections of S is an expander family if Iranges over square-free ideals of O K if d=2 and K is an arbitrary numberfield,or if d=3 and K=Q.

Author: ** Péter P. Varjú**

Source: https://arxiv.org/