ON THE POSSIBILITY OF GROUP-THEORETIC DESCRIPTION OF AN EQUIVALENCE RELATION CONNECTED TO THE PROBLEM OF COVERING SUBSETS IN FINITE FIELDS WITH COSETS OF LINEAR SUBSPACES - Sargsyan, D.S. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2019)
Let F^n_q be an n -dimensional vector space over a finite field F_q . Let C(F^n_q ) denote the set of all cosets of linear subspaces in F^n_q . Cosets H_1, H_2, … H_s are called exclusive if H_i subseteq H_j , 1 ≤ i < j ≤ s . A permutation f of C(F^n_q ) is called a C -permutation, if for any exclusive cosets H, H_1, H_2, … H_s such that H H_1 H_2 … H_s we have: i) cosets f(H), f(H_1), f(H_2), …, f(H_s) are exclusive; ii) cosets f^-1(H), f^-1(H_1), f^-1(H_2), …, f^-1(H_s) are exclusive; iii) f(H) f(H_1) f(H_2) … f(H_s) ; vi) f^-1(H) f^-1(H_1) f^-1(H_2) … f^-1(H_s) . In this paper we show that the set of all C -permutations of C(F^n_q ) is the General Semiaffine Group of degree n over F_q .