Growth in groups: ideas and perspectives

By Harald Andrés Helfgott. 2013

72 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/6c99b8e2ced9d36156c3e6121ec49c3af418f5e1

How researchers see this paper

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In Computational Theory and Mathematics

1. Ilya D. Shkredov
2. M. Rudnev
3. Oliver Roche-Newton
4. Brendan Murphy
5. Giorgis Petridis
6. Sophie Stevens

In Discrete Mathematics and Combinatorics

1. Ilya D. Shkredov
2. M. Rudnev
3. Brendan Murphy
4. Oliver Roche-Newton
5. Giorgis Petridis
6. Sophie Stevens
7. Frank de Zeeuw
8. Tom Sanders

Citations in the corpus

• NEW RESULTS ON SUM‐PRODUCT TYPE GROWTH OVER FIELDS (2017, methodology): “See, for example, a fairly recent review [16] by Helfgott for growth in Lie type groups.”