A New Type of Weakly Commutative Groups

Authors

  • Hariwan Z. Ibrahim University of Zakho
  • Muwafaq M. Salih University of Duhok

DOI:

https://doi.org/10.25271/2017.5.2.373

Keywords:

Wm-group, homomorphism, normal Wm- subgroup, kernel

Abstract

The aim of the present paper is to define and study a new class of groups, namely Wm-groups with a single binary operation based on axioms of semi commutativity, right identity and left inverse. Moreover, we introduce the notions of right cosets, quotient Wm-groups, homomorphisms, kernel and normal Wm-subgroups in terms of Wm-groups, and investigate some of their properties.

Author Biographies

Hariwan Z. Ibrahim, University of Zakho

Dept. of Mathematics, Faculty of Science, University of Zakho, Zakho, Kurdistan Region, Iraq

Muwafaq M. Salih, University of Duhok

Dept. of Mathematics, College of Basic Education, University of Duhok, Kurdistan Region, Iraq

References

M. R. Adhikari and A. Adhikari, Groups, Rings and Modules with Applications, 2nd edn. Universities Press, Hyderabad (2003).
M. R. Adhikari and A. Adhikari, Text Book of Linear Algebra: An Introduction to Modern Algebra. Allied Publishers, New Delhi (2004).
Clifford A. H. and Preston G. B., The Algebraic Theory of Semigroups, Vol. I, American Mathematical Society, Providence, R. I., (1961).

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Published

2017-06-30

How to Cite

Ibrahim, H. Z., & Salih, M. M. (2017). A New Type of Weakly Commutative Groups. Science Journal of University of Zakho, 5(2), 228–231. https://doi.org/10.25271/2017.5.2.373

Issue

Vol. 5 No. 2 (2017): June, 2017

Section

Science Journal of University of Zakho

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