Membership of A v G for classes of finite weakly abundant semigroups

TY - JOUR

T1 - Membership of A v G for classes of finite weakly abundant semigroups

AU - Fountain, John

AU - Gomes, Gracinda

AU - Gould, Victoria

PY - 2009/9

Y1 - 2009/9

N2 - We consider the question of membership of A V G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A V G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; we remark that any finite monoid with semilattice of idempotents is weakly abundant. To study such semigroups we develop a number of techniques that may be of interest in their own right.

AB - We consider the question of membership of A V G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A V G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; we remark that any finite monoid with semilattice of idempotents is weakly abundant. To study such semigroups we develop a number of techniques that may be of interest in their own right.

KW - weakly abundant

KW - band

KW - fundamental

KW - weakly adequate

KW - bountiful

KW - A V G

KW - ADEQUATE SEMIGROUPS

KW - PROPER COVERS

KW - IDEMPOTENTS

KW - MONOIDS

UR - http://www.scopus.com/inward/record.url?scp=71449109624&partnerID=8YFLogxK

U2 - 10.1007/s10998-009-9009-1

DO - 10.1007/s10998-009-9009-1

M3 - Article

SN - 1588-2829

VL - 59

SP - 9

EP - 36

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

IS - 1

ER -