English

Growth in groups: ideas and perspectives

Group Theory 2015-02-12 v7 Combinatorics Number Theory

Abstract

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear algebraic groups, with SL_2(Z/pZ) as the basic example, as well as permutation groups. The emphasis lies on the ideas behind the methods.

Keywords

Cite

@article{arxiv.1303.0239,
  title  = {Growth in groups: ideas and perspectives},
  author = {H. A. Helfgott},
  journal= {arXiv preprint arXiv:1303.0239},
  year   = {2015}
}

Comments

60 pages. This is the final version, incorporating corrections from the proofreaders. To appear in Bull. Am. Math. Soc

R2 v1 2026-06-21T23:35:09.656Z