On Non-Commutative Rhotrix Groups over Finite Fields

Abstract

This paper considers the pair (FGR_n(Z_p),^o) consisting of the set of all invertible rhotrices of size n over a finite field of integers moduloprime p and together with the binary operation of row-column based method for rhotrix multiplication; '^o' , in order to introduce concrete constructions of noncommutative rhotrix groups over finite fields. Furthermore, we pick specific groups (FGR₃(Z₂),^o), (FGR₃(Z₃),^o) and analyze them, so as to obtain their elements, multiplication tables, orders and subgroups. In the process, a number of theorems were developed.

Keywords: Groups, subgroups, finite rhotrix groups