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arXiv · 1803.03351

Expansion for the product of matrices in groups

Doowon Koh·Thang Pham·Chun-Yen Shen·Le Anh Vinh
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Abstract

In this paper, we give strong lower bounds on the size of the sets of products of matrices in some certain groups. More precisely, we prove an analogue of a result due to Chapman and Iosevich for matrices in $SL_2(\mathbb{F}_p)$ with restricted entries on a small set. We also provide extensions of some recent results on expansion for cubes in Heisenberg group due to Hegyv\'{a}ri and Hennecart.

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Doowon Koh, Thang Pham, Chun-Yen Shen, Le Anh Vinh. 2018-03-09. Expansion for the product of matrices in groups. https://arxiv.org/abs/1803.03351

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