Open AccessFormulation of the Nonabelian Tensor Square of a Bieberbach Group
Publication year - 2019
Publication title -
international journal of recent technology and engineering
Language(s) - English
Resource type - Journals
ISSN - 2277-3878
DOI - 10.35940/ijrte.b1046.0782s219
Subject(s) - mathematics , square (algebra) , tensor (intrinsic definition) , generalization , group (periodic table) , pure mathematics , set (abstract data type) , combinatorics , mathematical analysis , geometry , physics , quantum mechanics , computer science , programming language
A Bieberbach set can be categorized as a torsion free crystallographic set. Some properties can be explored from the set such as the property of nonabelian tensor square. The nonabelian tensor square is one type of the homological factors of sets. This paper focused on a Bieberbach set with C2 ×C2 as the point set of lowest dimension three. The purpose of this paper is to determine the generalization of the formula of the nonabelian tensor square of one Bieberbach set with point set C2 × C2of lowest dimension three which is denoted by S2 (3) up to dimensionn. The polycyclic presentation, the abelianization of S2 (3) and the central subgroup of the nonabelian tensor square of S2 (3) are also presented.