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
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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 (GRn(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 (GRn(F),⚬) and then advance to show that its particular subgroup is embedded in a particular subgroup of the well-known general linear group (GRn(F),•). Furthermore, we shall investigate isomorphic relationship between some subgroups of (GRn(F),⚬).

Keywords

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

AMS Classification

  • 20H30

References

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  2. 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.
  3. Sani, B. (2004) An alternative method for multiplication of rhotrices. Int. J. Math. Educ. Sci. Technol. 35, 777–781.
  4. Sani, B. (2007) The row-column multiplication for high dimensional rhotrices. Int. J. Math. Educ. Sci. Technol. 38, 657–662.
  5. Mohammed, A. (2007) Enrichment exercises through extension to rhotrices. Int. J. Math. Educ. Sci. Technol. 38, 131–136.
  6. 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

APA

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.

Chicago

Mohammed, A., and U. E. Okon. “On Subgroups of Non-commutative General Rhotrix Group.” Notes on Number Theory and Discrete Mathematics 22, no. 2 (2016): 72-90.

MLA

Mohammed, A., and U. E. Okon. “On Subgroups of Non-commutative General Rhotrix Group.” Notes on Number Theory and Discrete Mathematics 22.2 (2016): 72-90. Print.

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