Non-commutative finite monoids of a given order <i>n</i> ≥ 4

Ahmadi, B.; Campbell, C. M.; Doostie, H.

doi:10.2478/auom-2014-0028

Cited by 3 publications

(2 citation statements)

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“…Identifying a finite non-group semigroup (commutative or non-commutative) of order of a given positive integer n could be significant because of the interesting applications of finite semigroups in computer science, mathematics and finite machines. As a subclass of non-group semigroups, the non-commutative monoids of a given order were identified in 2014 by Ahmadi et al [2] to show that for every positive integer n ≥ 4, there exists a non-commutative monoid of order n. In this paper, we intend to identify two types of finite semigroups, commutative non-monoids of order p q and commutative monoids of order of a given positive integer n ≥ 4 . By giving the unique minimal generating set for the commutative non-monoids, we specify the number of all non-isomorphic semigroups of this type.…”

Section: Introductionmentioning

confidence: 99%

On the identification of finite non-group semigroups of a given order

Monsef

Doostie

2020

Math Sci

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Identifying finite non-group semigroups for every positive integer is significant because of many applications of such semigroups are functional in various branches of sciences such as computer science, mathematics and finite machines. The finite non-commutative monoids as a type of such semigroups were identified in 2014, for every positive integer. We here attempt to identify the finite commutative monoids and finite commutative non-monoids of a given integer n = p q , for every integers , ≥ 2 and different primes p and q. In order to recognize the commutative monoids, we present a class of 2-generated monoids of a given order, and for the commutative non-monoids of order n = p q , we give the minimal generating set. Moreover, we prove that there are exactly (p − 2)(q − 2) non-isomorphic commutative non-monoids of order p q. The identification of non-group semigroups for the integers p 2 and 2p is achieved. The automorphism groups of these groups are specified as well. As a result of this study, an interesting difference between the abelian groups and the commutative semigroups of order p 2 is presented.

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Section: Introductionmentioning

confidence: 99%

On the identification of finite non-group semigroups of a given order

Monsef

Doostie

2020

Math Sci

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“…The applications of various algebraic structures abound (see [1,2,3,6,7,8] for details and related references). In particular, certain algebraic structures have found applications in formal language theory (see [6] for details).…”

Section: Introductionmentioning

confidence: 99%