The $n$-Generalized Schützenberger-crossed product of monoids

Esra Kırmızı Çetinalp

doi:10.3842/umzh.v76i2.7535

Esra Kırmızı Çetinalp Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey University, Turkey

DOI: https://doi.org/10.3842/umzh.v76i2.7535

Keywords: Schützenberger product, crossed product, regularity

Abstract

UDC 512.5

We study the $n$-generalized Schützenberger-crossed product from the viewpoint of combinatorial group theory and define a new version of this product. For given monoids of this new product, we obtain a representation of the $n$-generalized Schützenberger-crossed product of arbitrary monoids.

References

A. L. Agore, G. Militaru, Crossed product of groups, applications, Arab. J. Sci. Eng., 33, 1–17 (2008).

A. L. Agore, D. Fratila, Crossed product of cyclic groups, Czech. Math. J., 60, 889–901 (2010) . DOI: https://doi.org/10.1007/s10587-010-0065-8

F. Ateş, Some new monoid and group constructions under semidirect product, Ars Combin., 91, 203–218 (2009).

F. Ateş, A. S. Şevik, Knit products of some groups and their applications, Rend. Semin. Mat. Univ. Padova, 2, 1–12 (2009). DOI: https://doi.org/10.4171/rsmup/121-1

E. K. Şetinalp, E. G. Karpuz, F. Ateş, A. S. Şevik, Two-sided crossed product of groups, Filomat, 30, № 4, 1005–1012 (2016). DOI: https://doi.org/10.2298/FIL1604005C

E. K. Şetinalp, E. G. Karpuz, Iterated crossed product of cyclic groups, Bull. Iran. Math. Soc., 44, № 6, 1493–1508 (2018). DOI: https://doi.org/10.1007/s41980-018-0103-0

E. K. Şetinalp, E. G. Karpuz, A. S. Şevik, Complete rewriting system for Schützenberger product of $n$ groups, Asian-Eur. J. Math., 12, № 1 (2019). DOI: https://doi.org/10.1142/S1793557119500128

E. K. Şetinalp, Regularity of $n$-generalized Schützenberger product of monoids, J. Balkesir University Institute of Science and Technology, 24, № 1 (2022). DOI: https://doi.org/10.25092/baunfbed.903026

E. K. Şetinalp, Regularity of iterated crossed product of monoids, Bull. Int. Math. Virtual Inst., 12, № 1, 151–158 (2022).

G. M. S. Gomes, H. Sezinando, J. E. Pin, Presentations of the Schützenberger product of $n$ groups, Commun. Algebra, 34, № 4, 1213–1235 (2006). DOI: https://doi.org/10.1080/00927870500454075

J. M. Howie, N. Ruškuc, Constructions and presentations for monoids, Commun. Algebra, 22, 6209–6224 (1994). DOI: https://doi.org/10.1080/00927879408825184

A. Emin, F. Ateş, S. İkikardeş, İ. N. Cangül, A new monoid construction under crossed products, J. Inequal. and Appl., 244 (2013). DOI: https://doi.org/10.1186/1029-242X-2013-244

E. G. Karpuz, F. Ateş, A. S. Şevik, Regular and $pi$-inverse monoids under Schützenberger products, Algebras, Groups and Geometries, 27, 455–471 (2010).

E. G. Karpuz, E. K. Şetinalp, Some remarks on the Schützenberger product of n monoids, Ric. Mat. (2022); doi/10.1007/s11587-022-00743-z. DOI: https://doi.org/10.1007/s11587-022-00743-z

M. P. Schützenberger, On finite monoids having only trivial subgroups, Inform. and Control, 8, 190–194 (1965). DOI: https://doi.org/10.1016/S0019-9958(65)90108-7

H. Straubing, A generalization of the Schützenberger product of finite monoids, Theoret. Comput. Sci., 13, 137–150 (1981). DOI: https://doi.org/10.1016/0304-3975(81)90036-0

M. A. Rudkovskii, Twisted product of Lie groups, Sib. Math. J., 38, 1120–1129 (1997). DOI: https://doi.org/10.1007/BF02673042