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The nonabelian tensor squares of one family of bieberbach groups with point group C2

Masri, Rohaidah and Aris, Nor'aini and Sarmin, Nor Haniza and Robert, Morse (2008) The nonabelian tensor squares of one family of bieberbach groups with point group C2. In: Advances In Fundamentals And Social Sciences. Penerbit UTM, Johor, pp. 69-81. ISBN 978-983-52-0609-2

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Abstract

The nonabelian tensor square, GѳG, of a group G is generated by the symbols g ѳ h , where g,hεG subject to the relations gg'ѳh=( ⁸g’ѳg⁸h)(gѳh) and gѳhh’=(gѳh)(hgѳhh') for all g,g',h,h'εG, where g g'=gg'g-1 is the conjugation on the left. The nonabelian tensor square is a special case of the nonabelian tensor product which has its origins in homotopy theory. The Bieberbach groups are extensions of a point group and a free abelian group of finite rank. The rank of the free abelian group is the dimension of a Bieberbach group. In this study, we will compute the nonabelian tensor square of one family of Bieberbach groups with cyclic point group of order 2 and dimension 3 or, denoted by . This group is polycyclic since it is an extension of polycyclic groups. The nonabelian tensor squares are obtained using computational method developed by R. Blyth and R. F. Morse in 2008 for polycyclic groups.

Item Type:Book Section
Uncontrolled Keywords:Bieberbach group, nonabelian tensor squares
Subjects:Q Science > Q Science (General)
ID Code:27835
Deposited By: Fazli Masari
Deposited On:17 Aug 2012 04:00
Last Modified:30 Apr 2013 06:41

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