On Subgroups of Non-Commutative Orthogonal Rhotrix Group

Abstract

This study investigates the algebraic structure of the noncommutative orthogonal rhotrix group under rhotrix row-column multiplication. The special orthogonal, diagonal orthogonal, and special diagonal orthogonal rhotrix groups are identified as subgroups, and their internal relationships are explicitly characterized through subgroup inclusions and intersections. In particular, it is shown that the orthogonal rhotrix group embeds as a subgroup of the general linear rhotrix group. To the best of our knowledge, this work provides the first systematic subgroup structural analysis of non-commutative orthogonal rhotrix groups. These results clarify the internal organization of orthogonal rhotrix groups and provide a foundational framework for further studies on normal subgroups, quotient structures, and related non-commutative rhotrix construction.