Iterated Crossed Product of Cyclic Groups

Abstract

In Panaite [Iterated crossed products, J. Algebra Appl. 13(7), 14580036 (2014)], Panaite studied iterated crossed product construction from the point of algebraic structures. In this paper, we study iterated crossed product from the point of Combinatorial Group Theory and define a new version of the crossed product of groups. First, we give some conditions for this new product to be a group, then we obtain a presentation for iterated crossed product of cyclic groups. Additionally, using this presentation, we find a complete rewriting system and thus we obtain normal form structure of elements of this new group construction. This gives us the solvability of the word problem for this product.

Crossed product of infinite groups and complete rewriting systems

“…The reader is referred to [7][8][9]11] for recent studies on crossed product of groups and its derivations.…”

Complete Rewriting System for Crossed Product of Infinite Groups

“…sorularını gündeme getirmektedir. Bu sorulara grup teori alanında verilen cevaplar olarak (Emin vd., 2013;Çetinalp, 2016;Çetinalp vd., 2016;Çetinalp ve Karpuz, 2018; Karpuz ve Çetinalp, 2018) çalışmalarına bakılabilir. Grup teorisinde yapılan bu çalışmalardan hareketle, bu çalışmada ilk olarak rankları (üreteç elemanların sayısı) 1 olan iki serbest grubun çapraz çarpımının monoid sunuşu için tam yeniden yazma sistemi bulunacaktır.…”