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.
Rank and status in semigroup theory / A. CHERUBINI; J. HOWIE; B. PIOCHI. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 32:(2004), pp. 2783-2801.
Rank and status in semigroup theory
PIOCHI, BRUNETTO
2004
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.
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