The Semigroup Efficiency of Direct Powers of Groups

Ayik, H.; Campbell, C. M.; O’Connor, John; Ruškuc, Nik

doi:10.1142/9789812792310_0002

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Cited by 4 publications

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“…In [2,3,4], efficient semigroup presentations for various groups are found. The groups considered include the finite abelian groups, dihedral groups, (projective) special linear groups and wreath products.…”

Section: Examplesmentioning

confidence: 99%

On defining groups efficiently without using inverses

Campbell

Mitchell

Ruškuc

2002

Math. Proc. Camb. Phil. Soc.

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Let G be a group, and let 〈A[mid ]R〉 be a finite group presentation for G with [mid ]R[mid ][ges ][mid ]A[mid ]. Then there exists a finite semigroup presentation 〈B[mid ]Q〉 for G such that [mid ]Q[mid ]- [mid ]B[mid ] = [mid ]R[mid ]- [mid ]A[mid ]. Moreover, B is either the same generating set or else it contains one additional generator.

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Section: Examplesmentioning

confidence: 99%

On defining groups efficiently without using inverses

Campbell

Mitchell

Ruškuc

2002

Math. Proc. Camb. Phil. Soc.

Self Cite

View full text Add to dashboard Cite

show abstract

“…On comparing the semigroup, monoids and groups defined by a presentation the articles [1,2,3,9] studied certain interesting classes of such algebraic structure. The references [6,7] study two special and outstanding classes of semigroups.…”

Section: Introductionmentioning

confidence: 99%