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2021•Journal of New Researches in MathematicsRequires access

The commutativity degree of semigroup of order p^α q^β

Mehrdad Azadi, M. Ghaneei

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Abstract

T‎he commutativity‎ degree of a finite non-commutative semigroup S is defined to be the probability‎ of choosing a pair (x,y) of the elements of S such that x commutes with y‎. Obviously if S is a abelian semigroup, then commutativity degree of S is 1. In this study, we consider semigroups are non-commutative and finite. ‎For a given positive integer n=p^α q^β where p and q are primes (2≤p

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T‎he commutativity‎ degree of a finite non-commutative semigroup S is defined to be the probability‎ of choosing a pair (x,y) of the elements of S such that x commutes with y‎. Obviously if S is a abelian semigroup, then commutativity degree of S is 1. In this study, we consider semigroups are non-commutative and finite. ‎For a given positive integer n=p^α q^β where p and q are primes (2≤p

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Available abstract

T‎he commutativity‎ degree of a finite non-commutative semigroup S is defined to be the probability‎ of choosing a pair (x,y) of the elements of S such that x commutes with y‎. Obviously if S is a abelian semigroup, then commutativity degree of S is 1. In this study, we consider semigroups are non-commutative and finite. ‎For a given positive integer n=p^α q^β where p and q are primes (2≤p

Key concepts: Commutative property, Semigroup, Mathematics, Abelian group, Degree (music), Order (exchange), Integer (computer science), Discrete mathematics

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