Iterated Bicrossed Product of Groups

Year 2022, Volume: 10 Issue: 1 , 134 - 137 , 15.04.2022

Esra Kırmızı Çetinalp

https://izlik.org/JA39RC52HK

Abstract

In [5], Cetinalp and Karpuz studied iterated crossed product contruction from the point of algebraic structures. In this paper, we study
iterated bicrossed product looking from the viewpoint of Combinatorial Group Theory and describe a new version of iterated bicrossed
product of groups. Also, we investigate that the group property of this new product is provided. Then, by considering finite cyclic groups, we
give an example for iterated bicrossed product of groups.

Keywords

Bicrossed product , group , semidirect product.

References

• [1] A. L. Agore, A. Chirvasitu, B. Ion, G. Militaru, Bicrossed products for finite groups, Algebr Represent Theor 12 (2009), 481-488.
• [2] F. Ates, Some new monoid and group constructions under semidirect products. Ars Comb., 91 (2009), 203-218.
• [3] D.C. Cohen and A.I. Suciu, Homology of iterated semidirect products of free groups, J. Pure Appl. Algebra, 126 (1998), 87–120.
• [4] E.K. C¸ etinalp, E.G. Karpuz, F. Ates¸, A.S. C¸ evik, Two-sided crossed product of groups, Filomat, 30(4) (2016), 1005–1012.
• [5] E.K. C¸ etinalp, E.G. Karpuz, Iterated crossed product of cyclic groups, Bulletin of the Iranian Mathematical Society, 44(6) ( 2018), 1493–1508.
• [6] E.K. C¸ etinalp, E.G. Karpuz, Crossed Product of Infinite Groups and Complete Rewriting Systems, Turkish Journal Of Mathematics, 45 (1) (2021), 410-422.
• [7] A. Emin, F. Ates, S. Ikikardes, I. N. Cangul, A new monoid construction under crossed products, Journal of Inequalities and Applications 244 (2013).
• [8] F. Panaite, Iterated crossed products, J. Algebra Appl., 13(7) (2014).
• [9] J.M. Howie and N. Ruskuc, Constructions and presentations for monoids, Comm. in Algebra 22 (15) (1994), 6209-6224.
• [10] P. W. Michor, Knit products of graded Lie algebras and groups, Suppl. Rendiconti Circolo Matematico di Palermo Ser. II, 22 (1989), 171-175.
• [11] M. Takeuchi, Matched pairs of groups and bismah product of Hopf algrebras, Comm. Algebra, 9(8)(1981), 841-882.
• [12] S. O. Unal, Green’s relations on ternary semihypergroups and crossed hyperproduct of hypergroups, Asian-European Journal of Mathematics, 14(7) (2021).
• [13] G. Zappa, Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili tra loro, Atti Secondo Congresso Un.Mat Ital. Bologna, (1940), 119-125.