Computing the Certain subgroups of the group D _2n × C _p , p is an Odd Prime Number

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.