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)**

## Details

### Authors and affiliations

A. Mohammed

*Department of Mathematics, Ahmadu Bello University
Zaria, Nigeria
*

U. E. Okon

*Department of Mathematics, Ahmadu Bello University*

Zaria, Nigeria

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

- Ajibade, A. O. (2003) The concept of rhotrix in mathematical enrichment. Int. J. Math. Educ. Sci. Technol. 34, 175–179.
- Atanassov, K. T., & Shannon, A. G. (1998) Matrix-tertions and matrix noitrets: exercises in mathematical enrichment. Int. J. Math. Educ. Sci. Technol. 29, 898–903.
- Sani, B. (2004) An alternative method for multiplication of rhotrices. Int. J. Math. Educ. Sci. Technol. 35, 777–781.
- Sani, B. (2007) The row-column multiplication for high dimensional rhotrices. Int. J. Math. Educ. Sci. Technol. 38, 657–662.
- Mohammed, A. (2007) Enrichment exercises through extension to rhotrices. Int. J. Math. Educ. Sci. Technol. 38, 131–136.
- Mohammed, A., Balarabe, M. & Imam, A. T. (2014) On construction of rhotrix semigroup. Journal of the Nigerian Association of Mathematical Physics, 27(3), 69–76.

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## Cite this paper

Mohammed, A., & Okon, U. E. (2016). On subgroups of non-commutative general rhotrix group. *Notes on Number Theory and Discrete Mathematics*, 22(2), 72-90.