On subgroups of non-commutative general rhotrix group

A. Mohammed and U. E. Okon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 2, Pages 72–90
Full paper (PDF, 208 Kb)

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Authors and affiliations

A. Mohammed
Department of Mathematics, Ahmadu Bello University
Zaria, Nigeria

U. E. Okon
Department of Mathematics, Ahmadu Bello University
Zaria, Nigeria

Abstract

This paper considers the pair (GR_n(F),⚬) 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 method for rhotrix multiplication; in order to introduce it as the concept of “non-commutative general rhotrix group”. We identify a number of subgroups of (GR_n(F),⚬) 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),•). Furthermore, we shall investigate isomorphic relationship between some subgroups of (GR_n(F),⚬).

Keywords

• Rhotrix
• Matrix
• Group
• Subgroup
• General rhotrix group
• General linear group

AMS Classification

• 20H30

References

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