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

Access to Document

10.1007/s00233-011-9352-4

Cite this

@article{a3dd4957b0814f2e86156baa2cb88f15,

title = "On the growth of generating sets for direct powers of semigroups",

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.",

keywords = "Semigroup, Monoid, Direct Power, Generating Set",

author = "Hyde, {James T.} and Loughlin, {Nicholas J.} and Martyn Quick and Nik Ru{\v s}kuc and Alistair Wallis",

year = "2012",

month = feb,

doi = "10.1007/s00233-011-9352-4",

language = "English",

volume = "84",

pages = "116--130",

journal = "Semigroup Forum",

issn = "0037-1912",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - On the growth of generating sets for direct powers of semigroups

AU - Hyde, James T.

AU - Loughlin, Nicholas J.

AU - Quick, Martyn

AU - Ruškuc, Nik

AU - Wallis, Alistair

PY - 2012/2

Y1 - 2012/2

N2 - 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.

AB - 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.

KW - Semigroup

KW - Monoid

KW - Direct Power

KW - Generating Set

U2 - 10.1007/s00233-011-9352-4

DO - 10.1007/s00233-011-9352-4

M3 - Article

SN - 0037-1912

VL - 84

SP - 116

EP - 130

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

On the growth of generating sets for direct powers of semigroups

Abstract

Keywords

Access to Document

Fingerprint

Cite this