Eylem GÜZEL KARPUZ, Esra KIRMIZI ÇETİNALP

Crossed product of infinite groups and complete rewriting systems

The aim of this paper is to obtain a presentation for crossed product of some infinite groups and then find its complete rewriting system. Hence, we present normal form structure of elements of crossed product of infinite groups which yield solvability of the word problem.

PDF

___

[1] Agore AL, Militaru G. Crossed product of groups, applications. Arabian Journal for Science and Engineering 2008; 33: 1-17.
[2] Agore AL, Fratila D. Crossed product of cyclic groups. Czechoslovak Mathematical Journal 2010; 60: 889-901.
[3] Ateş F. Some new monoid and group constructions under semidirect product. Ars Combinatoria 2009; 91: 203-218.
[4] Ateş F, Çevik AS. Knit products of some groups and their applications. Rendiconti del Seminario Matematico della Universita di Padova 2009; 2: 1-12.
[5] Book RV, Otto F. String-Rewriting Systems. New York, NY, USA: Springer-Verlag, 1993.
[6] Cangül İN, Çevik AS, Şimşek Y. A new approach to connect algebra with analysis: relationships and applications between presentations and generating functions. Boundary Value Problems 2013; 51: 1-17.
[7] Çetinalp EK, Karpuz EG, Ateş F, Çevik AS. Two-sided crossed product of groups. Filomat 2016; 30 (4): 1005-1012.
[8] Çetinalp EK, Karpuz EG, Iterated crossed product of cyclic groups. Bulletin of the Iranian Mathematical Society 2018; 44 (6): 1493-1508.
[9] Emin A, Ateş F, İkikardeş S, Cangül İN. A new monoid construction under crossed product. Journal of Inequalities and Applications 2013; 244.
[10] Hölder, O. Bildung zusammengesetzter gruppen. Mathematische Annalen 1895; 46: 321-422 (in German).
[11] Karpuz EG, Çetinalp EK. Growth series of crossed and two-sided crossed products of cyclic groups, Mathematica Slovaca 2018; 68 (3): 1-12.
[12] Rudkovskii MA. Twisted product of Lie groups. Siberian Mathematical Journal 1997; 38: 1120-1129.
[13] Sims CC. Computation for Finitely Presented Groups. Cambridge University Press, 1994.
[14] Taback J. An Introduction to Lamplighter Groups. Bowdoin University, 2011.