Commutativity Degree of Certain Finite AC-Groups

Document Type : Original Scientific Paper

Authors

Department of Mathematics, Faculty of Sciences, Arak University, Arak, I. R. Iran

Abstract

 For a finite group G, the probability of two elements of G that commute is the commutativity degree of G denoted by P(G). As a matter of fact, if C = {(a; b) ∈ G×G | ab = ba}, then P(G) = |C|/|G|2 . In this paper, we are going to find few formulas for P(G) independent of  |C|; for some AC-groups, and also in some special cases of finite minimal non-abelian groups. Moreover, the study will present implications for certain qualified finite groups.

Keywords

References

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Mathematics Interdisciplinary Research
Volume 6, Issue 4
December 2021
Pages 309-317

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