Author:
Mehdi H. J.,Shelash H. B.
Abstract
Abstract
Let τ(n) is the number of all divisors of n and σ(n) is the number of summation of all divisors n, Cavior, presented the number of all subgroups of the dihedral group is equal by τ(n) + σ(n). We in this paper determines a formula for the number of subgroups, normal and cyclic subgroups of the group G = D
2n
× C
p
= 〈a, b, c|a
n
= b
2 = c
p
, b
a
b = a
−1, [a, c] = [b, c] = 1〉, where p is an odd prime number.
Subject
General Physics and Astronomy
Reference18 articles.
1. Counting the subgroups of some finite groups;Calhoun;Amer. Math. Monthly,1987
2. The subgroups of the dihedral groups;Cavior;Math. Mag.,1975
3. Symmetry classes of tensors associated with the semi − dihedral groups SD8n;Hormozi;Colloq. Math.,2013
4. A Number-Theoretic Approach to Subgroups of Dihedral Groups;Jensen;SUT J. Math.,1990