Rank and Status in Semigroup Theory

Abstract

For each generating set A of a finite semigroup S the integer Δ(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|Δ(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.

Key Words:

• Finite semigroup
• Rank
• Status

1991 Mathematics Subject Classification:

• 20M10

Acknowledgments

Notes

^#Communicated by P. Higgins.