Multiplicative degree of some dihedral groups | Zendy

Norarida Abd Rhani | Zendy; Nor Muhainiah Mohd Ali | Zendy; Nor Haniza Sarmin | Zendy; Ahmad Erfanian | Zendy; Muhanizah Abdul Hamid | Zendy

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Multiplicative degree of some dihedral groups

Author(s) -

Norarida Abd Rhani,

Nor Muhainiah Mohd Ali,

Nor Haniza Sarmin,

Ahmad Erfanian,

Muhanizah Abdul Hamid

Publication year - 2016

Publication title -

aip conference proceedings

Language(s) - English

Resource type - Conference proceedings

eISSN - 1551-7616

pISSN - 0094-243X

DOI - 10.1063/1.4954591

Subject(s) - dihedral group , degree (music) , multiplicative function , mathematics , commutative property , group (periodic table) , dihedral angle , normal subgroup , combinatorics , multiplicative group , finite group , discrete mathematics , product (mathematics) , physics , mathematical analysis , geometry , hydrogen bond , quantum mechanics , molecule , acoustics

Let G be a group and H any subgroup of G. The commutativity degree of a finite group G is defined as the probability that a pair of elements x and y, chosen randomly from a group G, commute. The concept of commutativity degree has been extended to the relative commutativity degree of a subgroup H, which is defined as the probability that a random element of a subgroup, H commutes with another random element of a group G. This research extends the concept of relative commutativity degree to the multiplicative degree of a group G, which is defined as the probability that the product of a pair of elements x, y chosen randomly from a group G, is in H. This research focuses on some dihedral groups.

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