Open AccessConsistency Relations of an Extension Polycyclic Free Abelian Lattice Group by Quaternion Point Group
Author(s) -
Siti Afiqah Mohammad,
Nor Haniza Sarmin,
Hazzirah Izzati Mat Hassim
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1988/1/012071
Subject(s) - quaternion , abelian group , g module , mathematics , group (periodic table) , pure mathematics , torsion (gastropod) , quaternion group , elementary abelian group , lattice (music) , rank of an abelian group , torsion subgroup , extension (predicate logic) , algebra over a field , physics , computer science , quantum mechanics , geometry , automorphism , alternating group , biology , zoology , acoustics , programming language
An extension of a free abelian lattice group by finite group is a torsion free crystallographic group. It expounds its symmetrical properties or known as homological invariants. One of the methods to compute its homological invariants is by determining the polycyclic presentation of the group. These polycyclic presentations are first shown to satisfy its consistency relations. Therefore, our focus is to show that this extension polycyclic free abelian lattice group by quaternion point group satisfy its consistency relations.