Crecimiento y expansion en SL_2

TL;DR

This paper introduces the concept of growth in finite groups, focusing on SL_2, highlighting developments from 2005 to 2015, with an emphasis on combinatorial approaches and minimal algebraic background.

Contribution

It provides an accessible overview of recent growth results in SL_2, emphasizing combinatorial methods and presenting proofs in a generalizable, abstract manner.

Findings

Summarizes key growth results in SL_2 from 2005 to 2015

Highlights combinatorial techniques in group growth

Provides accessible proofs with minimal algebraic prerequisites

Abstract

This is a short introduction (in Spanish) to the study of growth in finite groups, with SL_2 as an example. Emphasis is put on developments of the decade 2005--2015, originating partly in combinatorics. Little algebraic-geometrical background is assumed, but the proofs are nevertheless presented in a relatively abstract and generalizable way.