On the growth of generating sets for direct powers of semigroups

James T. Hyde; Nicholas J. Loughlin; Martyn Quick; Nik  Ruškuc; Alistair Wallis

doi:10.1007/s00233-011-9352-4

On the growth of generating sets for direct powers of semigroups

James T. Hyde
, Nicholas J. Loughlin
, Martyn Quick
, Nik Ruškuc
, Alistair Wallis

School of Mathematical & Computer Sciences

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

3 Citations (Scopus)

Abstract

For a semigroup S its d-sequence is d(S) = (d₁, d₂, d₃, . . .), where d_i is the smallest number of elements needed to generate the ith direct power of S. In this paper we present a number of facts concerning the type of growth d(S) can have when S is an infinite semigroup, comparing them with the corresponding known facts for infinite groups, and also for finite groups and semigroups.

Original language	English
Pages (from-to)	116-130
Number of pages	15
Journal	Semigroup Forum
Volume	84
Issue number	1
DOIs	https://doi.org/10.1007/s00233-011-9352-4
Publication status	Published - Feb 2012

Keywords

Semigroup
Monoid
Direct Power
Generating Set

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10.1007/s00233-011-9352-4

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abstract = "For a semigroup S its d-sequence is d(S) = (d1, d2, d3, . . .), where di is the smallest number of elements needed to generate the ith direct power of S. In this paper we present a number of facts concerning the type of growth d(S) can have when S is an infinite semigroup, comparing them with the corresponding known facts for infinite groups, and also for finite groups and semigroups.",

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AU - Ruškuc, Nik

AU - Wallis, Alistair

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KW - Semigroup

KW - Monoid

KW - Direct Power

KW - Generating Set

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VL - 84

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JO - Semigroup Forum

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On the growth of generating sets for direct powers of semigroups

Abstract

Keywords

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