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GROWTH IN SOME FINITE THREE-DIMENSIONAL MATRIX GROUPS.
- Source :
-
SIAM Journal on Discrete Mathematics . 2020, Vol. 34 Issue 3, p1984-1998. 15p. - Publication Year :
- 2020
-
Abstract
- We study the growth of product sets in some finite three-dimensional matrix groups. In particular, we prove two results about the group of 2 × 2 upper triangular matrices over arbitrary finite fields: a product set estimate using techniques from multiplicative combinatorics and an energy estimate using incidence geometry. The energy method gives better quantitative results but only applies to small sets. We also prove an energy result for the Heisenberg group. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 34
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 147892640
- Full Text :
- https://doi.org/10.1137/20M1338265