Q-Soft Normal Subgroups

Abstract

This paper contains some definitions and results in Q-soft normal subgroup theory and cosets. Also some results are introduced  which have been used by homomorphism and anti-homomorphism of Q-soft normal subgroups. Next  we prove the analogue of the Lagrange's theorem.

Keywords

• Q-soft subsets,group theory,Q-soft subgroups,Q-soft normal subgroups,homomor- phism

References

1. [1] H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci., 177(2007), 2726-2735.
2. [2] M. I. Ali, F. Feng, X. Y. Liu, W. K. Min, and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57(2008), 2621-2628.
3. [3] M. Aslam and S. M. Qurashi, Some contributions to soft groups,Ann. Fuzzy Maths. Inform., 4(2012), 177-195.
4. [4] D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parameterization reduction of soft sets and its applications, Comput. Math. Appl., 49(2005), 757-763.
5. [5] F. Hassani and R. Rasuli, Q-soft Subgroups and Anti-Q-soft Subgroups in Universal Algebra, The Journal of Fuzzy Mathematics Los Angeles 26 (1) (2018), 139-152.
6. [6] T. Hungerford, Algebra, Graduate Texts in Mathematics. Springer (2003).
7. [7] A. Kharal and B. Ahmad, Mappings on Soft Classes, New Mathematics and Natural Computation 7 (3) (2011).
8. [8] P. K. Maji, R. Biswas and A. R. Roy, Sof tset theory, Computer Mathematics with Applications, 45 (2003), 555-562.

9. [9] P. K. Maji, R. Biswas and A. R. Roy, An application of soft sets in a decision making problem, Computer Mathematics with Applications, 44 (2002), 1007-1083.
10. [10] D. A. Molodtsov, Soft set theory-First results, Computers and Mathematics with Applications 37 (4) (1999), 19-31.
11. [11] D. A. Molodtsov, The theory of soft sets (in Russian), URSS Publishers Moscow, 2004.
12. [12] R. Rasuli, Extension of Q-soft ideals in semigroups, Int. J. Open Problems Compt. Math., 10 (2) (2017), 6-13.
13. [13] R. Rasuli, Soft Lie Ideals and Anti Soft Lie Ideals, The Journal of Fuzzy Mathematics Los Angeles 26 (1) (2018),193-202.
14. [14] A. Solairaju and R. Nagarajan, A New structure and constructions of Q-fuzzy groups, Advances in fuzzy mathematics 4 (2009), 23-29.