Open AccessThe cyclic Decomposition of the Factor Group ∁F(2 2k×D4, ℤ)/ ρ¯ (2 2k×D4) When κ is a prime Number
Author(s) -
Naba Hasoon Jabir
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 - 10.1088/1742-6596/1818/1/012018
Subject(s) - order (exchange) , dihedral group , group (periodic table) , prime (order theory) , combinatorics , mathematics , crystallography , physics , chemistry , quantum mechanics , finance , economics
In this paper we find the Circular Divison of The ℱactor G roup cℱ( 2 2κ ×D4, ℤ)/ ρ ¯ ( 2 2κ ×D4) when κ is a prime number, where 2 2κ is denoted to Quaternion group of order 4k, such that for each positive integer n, there are two generators X and Y for 2 2κ satisfies Q2k={ X i Y j, 0≤ i ≤ 2κ − 1, j=0, 1} which has the following properties{ X 2k= Y 4=I, Y X k Y -1= X -k} and D4 is the Dihedral group of order 8 is generate by a rotation e of order 4 and reflection f of order 2 then 8 elements of D4 can be written as: {I*, e, e2, e3, f, fe, fe2, fe3}.