On Subgroups of Non-Commutative General Rhotrix Group

Abstract

This paper considers the pair (GR_n(F),^o) consisting of the set of all invertible rhotrices of size n over an arbitrary field F; and together with the binary operation of row-column based method for rhotrix multiplication; '^o' , in order to introduce it as the concept of “non commutative general rhotrix group”. We identify a number of subgroups of (GR_n(F),^o)  and then advance to show that its particular subgroup is embedded in a particular subgroup of the well-known general linear group (GR_n(F),^o). Furthermore, we shall investigate isomorphic relationship between some subgroups of  (GR_n(F),^o) .

Keywords: Rhotrix, matrix, group, rhotrix groups, matrix groups, general rhotrix group, general linear group