Rank and status in semigroup theory

A  Cherubini; J M  Howie; B  Piochi

doi:10.1081/AGB-120037416

Rank and status in semigroup theory

A Cherubini, J M Howie, B Piochi

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For each generating set A of a finite semigroup S the integer Delta(A) is defined as the least n for which every element of S is expressible as a product of at most n elements of A. The status of S is defined as the least value of \A\Delta(A) among generating sets of A. Some general bounds are obtained, and the notion is explored in more detail for certain well understood classes of semigroups.

Original language	English
Pages (from-to)	2783-2801
Number of pages	19
Journal	Communications in Algebra
Volume	32
DOIs	https://doi.org/10.1081/AGB-120037416
Publication status	Published - 2004

Keywords

finite semigroup
rank
status
FINITE-GROUPS
THIN BASES

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10.1081/AGB-120037416

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abstract = "For each generating set A of a finite semigroup S the integer Delta(A) is defined as the least n for which every element of S is expressible as a product of at most n elements of A. The status of S is defined as the least value of \A\Delta(A) among generating sets of A. Some general bounds are obtained, and the notion is explored in more detail for certain well understood classes of semigroups.",

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AU - Howie, J M

AU - Piochi, B

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AB - For each generating set A of a finite semigroup S the integer Delta(A) is defined as the least n for which every element of S is expressible as a product of at most n elements of A. The status of S is defined as the least value of \A\Delta(A) among generating sets of A. Some general bounds are obtained, and the notion is explored in more detail for certain well understood classes of semigroups.

KW - finite semigroup

KW - rank

KW - status

KW - FINITE-GROUPS

KW - THIN BASES

U2 - 10.1081/AGB-120037416

DO - 10.1081/AGB-120037416

M3 - Article

SN - 0092-7872

VL - 32

SP - 2783

EP - 2801

JO - Communications in Algebra

JF - Communications in Algebra

ER -

Rank and status in semigroup theory

Abstract

Keywords

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