On Subgroups of Non-Commutative Orthogonal Rhotrix Group

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Published: 31-12-2025
DOI: https://doi.org/10.5281/zenodo.18110646
Keywords:
General rhotrix group, embedding, general linear group, group homomorphism, rhotrix multiplication

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Bayo Musa Ahmed
University of Ilorin
Mercy A. Agboola
Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, Nigeria
Isa Abubakar
Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, Nigeria.

Abstract

This study investigates the algebraic structure of the non-commutative 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.

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Vol. 5 No. 1 (2025): Special Issue

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Articles
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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On Subgroups of Non-Commutative Orthogonal Rhotrix Group. (2025). Al-Hikmah Journal of Pure and Applied Sciences (AJPAS) , 5(1). https://doi.org/10.5281/zenodo.18110646

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