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Hegyvari and Hennecart showed that if $B$ is a sufficiently large brick of a Heisenberg group, then the product set $Bcdot B$ contains many cosets of the center of the group. We give a new, robust proof of this theorem that extends to all extra special groups as well as to a large family of quasigroups.
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 entrie
Let $A$ be a compact set in $mathbb{R}$, and $E=A^dsubset mathbb{R}^d$. We know from the Mattila-Sjolins theorem if $dim_H(A)>frac{d+1}{2d}$, then the distance set $Delta(E)$ has non-empty interior. In this paper, we show that the threshold $frac{d+1}{2d}$ can be improved whenever $dge 5$.
In analogy with epsilon-biased sets over Z_2^n, we construct explicit epsilon-biased sets over nonabelian finite groups G. That is, we find sets S subset G such that | Exp_{x in S} rho(x)| <= epsilon for any nontrivial irreducible representation rho.
The importance of the Hurwitz Metzler matrices and the Hurwitz symmetric matrices can be appreciated in different applications: communication networks, biology and economics are some of them. In this paper, we use an approach of differential topology
This paper studies the maximal size of product-free sets in Z/nZ. These are sets of residues for which there is no solution to ab == c (mod n) with a,b,c in the set. In a previous paper we constructed an infinite sequence of integers (n_i)_{i > 0} an