Growth in groups: ideas and perspectives
Copyright policy )Growth in groups: ideas and perspectives
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.
60 pages. This is the final version, incorporating corrections from the proofreaders. To appear in Bull. Am. Math. Soc
- University of Göttingen Germany
- École Normale Supérieure France
growth, permutation groups, Group Theory (math.GR), Linear algebraic groups over finite fields, FOS: Mathematics, Mathematics - Combinatorics, General theory for finite permutation groups, Number Theory (math.NT), Arithmetic and combinatorial problems involving abstract finite groups, Mathematics - Number Theory, non-commutative groups, Arithmetic combinatorics; higher degree uniformity, Asymptotic properties of groups, \( \mathrm {SL}_2(\mathbb{Z}/p\mathbb{Z})\), additive combinatorics, Combinatorics (math.CO), Mathematics - Group Theory, 20F69, 20D60, 11B30, 20B05, 05C25, linear algebraic groups
growth, permutation groups, Group Theory (math.GR), Linear algebraic groups over finite fields, FOS: Mathematics, Mathematics - Combinatorics, General theory for finite permutation groups, Number Theory (math.NT), Arithmetic and combinatorial problems involving abstract finite groups, Mathematics - Number Theory, non-commutative groups, Arithmetic combinatorics; higher degree uniformity, Asymptotic properties of groups, \( \mathrm {SL}_2(\mathbb{Z}/p\mathbb{Z})\), additive combinatorics, Combinatorics (math.CO), Mathematics - Group Theory, 20F69, 20D60, 11B30, 20B05, 05C25, linear algebraic groups
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