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Moradipour, Kayvan; Sarmin, Nor Haniza; Erfanian, Ahmad

doi:10.2306/scienceasia1513-1874.2012.38.113

Cited by 7 publications

(3 citation statements)

References 16 publications

(16 reference statements)

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“…Proof : Suppose that G 1 and G 2 are two groups of Case I, using the proof of Theorem 4 in Ref. 12, we have k(G 1 ) = k(G 2 ). Now, by applying Proposition 1 and (4), we obtain…”

Section: Propositionmentioning

confidence: 99%

Some results on the non-commuting graph of a finite group

Moradipour¹,

Ilangovanb²,

Rashidc³

2019

ScienceAsia

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Let G be a metacyclic p-group, and let Z(G) be its center. The non-commuting graph Γ G of a metacyclic pgroup G is defined as the graph whose vertex set is G−Z(G), and two distinct vertices x and y are connected by an edge if and only if the commutator of x and y is not the identity. In this paper, we give some graph theoretical properties of the non-commuting graph Γ G . Particularly, we investigate planarity, completeness, clique number and chromatic number of such graph. Also, we prove that if G 1 and G 2 are isoclinic metacyclic p-groups, then their associated graphs are isomorphic.

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“…Proof : Suppose that G 1 and G 2 are two groups of Case I, using the proof of Theorem 4 in Ref. 12, we have k(G 1 ) = k(G 2 ). Now, by applying Proposition 1 and (4), we obtain…”

Section: Propositionmentioning

confidence: 99%

Some results on the non-commuting graph of a finite group

Moradipour¹,

Ilangovanb²,

Rashidc³

2019

ScienceAsia

Self Cite

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“…Furthermore, You et al [17] classified the groups in which conjugacy classes are not set-wise relatively prime for any four distinct classes. Moreover, Moradipouret al [18] used the conjugacy class graph to find some graph properties of some finite metacyclic 2-groups. Omer et al [9] extended the work in [8] and defined the generalized conjugacy class graph denoted by .…”

Section: -2mentioning

confidence: 99%

Groups and graphs in probability theory

Sarmin¹,

El-Sanfaz

Omer

2016

AIP Conference Proceedings

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Abstract. In this paper, G denotes a dihedral group of order 2n and denotes the set of all subsets of all commuting elements of size two in the form of , , a b where a and b commute and 2. a bBy extending the concept of commutativity degree, the probability that an element of a group fixes a set can be acquired using the group actions on set. In this paper, the probability that an element of G fixes the set under regular action is computed. The results obtained are then applied to graph theory, more precisely to generalized conjugacy class graph and orbit graph.

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“…More recently, [12] obtained the exact value of the commutativity degree of the generalized quaternion groups, dihedral groups, semidihedral groups and quasi dihedral groups. More researches related to commutativity degree of groups and their extension can be found in [ [11], [15], [14], [13], [4], [7]]. The previous concepts of the mention researches are strictly associated with the conception of commutativity degree of a group.…”

Section: Introductionmentioning

confidence: 99%

The Order Product Prime Probability and Commutativity Degree for Some Finite Groups

Ali¹,

Isah²,

Bello³

2022

MJMS

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Statistical approach often provides techniques in exploring more on the algebraic properties of finite groups. In this paper, two new group probabilities are defined in which the group elements having certain common characteristics are considered. Let G be a finite group, the order product prime probability is defined as the probability that two randomly selected elements x and y in G satisfy |x||y|=ps and the order product prime commutativity degree is the probability that elements satisfying the above property commutes. Some formulas for computing these probabilities for dihedral groups are obtained.

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Abstract: Let G be a finite non-abelian metacyclic p-group where p is any prime. We compute the exact number of conjugacy classes and the commutativity degree of G. In particular, we describe the number of conjugacy classes both in the split and non-split case.

Cited by 7 publications

References 16 publications

Some results on the non-commuting graph of a finite group

Some results on the non-commuting graph of a finite group

Groups and graphs in probability theory

The Order Product Prime Probability and Commutativity Degree for Some Finite Groups

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