Keywords:-
Keywords:
Right loops, Group Torsion, Isomorphic classes, Deformation of operation
Article Content:-
Abstract
In this article, we find formula for non-isomorphic right loops of order n by operation ◦g will be termed as the deformation of ◦ through the map g: S → Sym(S) with g(e) = I.
References:-
References
[1] A. A. Albert, “Quasigroup I”, Trans. Amer. Math. Soc., 54(1943), 507-519.
[2] A. A. Albert, “Quasigroup II”, Trans. Amer. Math. Soc., 55(1944),401-419.
[3] A. A. Ungar,” Weakly Associative Groups”, Resultes in Mathematics,17(1990), 150 – 168.
[4] A. C. Yadav and V. Kakkar, “Public key exchange using right transversals and right loops”, Journal of Discrete Mathematical Sciences and Cryptography, 20.
5(2017), 1207 − 1215.
[5] GAP Software 4.11.1.
[6] R. Baer, “Nets and groups”, Trans. Amer. Soc. 46(1939), 110-141.
[7] R. H. Bruck, “Contributions to the theory of Loops”, Trans. Amer. Math. Soc., 60(1946), 245-354.
[8] R. Lal,” Transversals in groups”, Journal of algebra, 181(1996), 70 − 81.
[9] R. Lal and A. C. Yadav, “Twisted Automorphisms and Twisted Right Gyrogroups”, Communications in Algebra, 43:8(2015), 3442-3458.
[10] R. Lal and A. C. Yadav, “Topological Right Gyrogroups and Gyrotransversals”, Communications in Algebra, 41:9(2013), 3559 − 3575.
[11] V. Kakkar and R. P. Shukla,” On the number of isomorphism classes of transversals”, Proc. Indian Acad. Sci. (Math. Sci.), 123(2012), 345 − 359.
[12] V. K. Jain and R. P. Shukla, “On the Isomorphism Classes of Transversals-II”, Communications
in Algebra, 39:6(2011), 2024-2036.
[2] A. A. Albert, “Quasigroup II”, Trans. Amer. Math. Soc., 55(1944),401-419.
[3] A. A. Ungar,” Weakly Associative Groups”, Resultes in Mathematics,17(1990), 150 – 168.
[4] A. C. Yadav and V. Kakkar, “Public key exchange using right transversals and right loops”, Journal of Discrete Mathematical Sciences and Cryptography, 20.
5(2017), 1207 − 1215.
[5] GAP Software 4.11.1.
[6] R. Baer, “Nets and groups”, Trans. Amer. Soc. 46(1939), 110-141.
[7] R. H. Bruck, “Contributions to the theory of Loops”, Trans. Amer. Math. Soc., 60(1946), 245-354.
[8] R. Lal,” Transversals in groups”, Journal of algebra, 181(1996), 70 − 81.
[9] R. Lal and A. C. Yadav, “Twisted Automorphisms and Twisted Right Gyrogroups”, Communications in Algebra, 43:8(2015), 3442-3458.
[10] R. Lal and A. C. Yadav, “Topological Right Gyrogroups and Gyrotransversals”, Communications in Algebra, 41:9(2013), 3559 − 3575.
[11] V. Kakkar and R. P. Shukla,” On the number of isomorphism classes of transversals”, Proc. Indian Acad. Sci. (Math. Sci.), 123(2012), 345 − 359.
[12] V. K. Jain and R. P. Shukla, “On the Isomorphism Classes of Transversals-II”, Communications
in Algebra, 39:6(2011), 2024-2036.
Downloads
Citation Tools
How to Cite
Kushwaha, S., & Yadav, A. C. (2025). On Isomorphism Classes of Right Loops. International Journal Of Mathematics And Computer Research, 13(5), 5175-5177. https://doi.org/10.47191/ijmcr/v13i5.06