Work

Sets preserved by a large subgroup of the special linear group

Year: 2026

Type: article

Abstract: Let be a subset of the affine plane over a finite field . We bound the size of the subgroup of that preserves . Specifically, there exists a constant such that for any , if is preserved by more than elements of , then is contained in a line through the origin. This result is sharp in general, and will be proved by using combinatorial arguments and applying a point‐line incidence bound in due to Mockenhaupt and Tao (2004).

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70298

Authors: Thang Pham, Le Quang‐Hung, Kaloyan Slavov

Institutions: Xidian University, Trường Đại học Khoa học và Công nghệ Hà Nội, Hanoi University of Science and Technology, ETH Zurich

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: European Research Council