Special Issue: International Conference on Semigroups and Groups in Honor of the 65th Birthday of Prof. John RhodesNo Access

ON SEMIGROUPS WHOSE IDEMPOTENT-GENERATED SUBSEMIGROUP IS APERIODIC

MANUEL DELGADO

Centro de Matemática, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

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VÍTOR H. FERNANDES

Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte de Caparica, 2829-516 Caparica, Portugal

C.A.U.L., Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

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STUART MARGOLIS

Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel

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, and

BENJAMIN STEINBERG

Carleton University, School of Mathematics & Statistics, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada

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https://doi.org/10.1142/S021819670400202XCited by:5 (Source: Crossref)

Abstract

We show that if S is a finite semigroup with aperiodic idempotent-generated subsemigroup and H is a pseudovariety of groups, then the sequence of iterated H-kernels of S stops at the idempotent-generated subsemigroup if and only if each subgroup of S belongs to the wreath product closure of H. Applications are given to Mal'cev products.

Keywords:

AMSC: 20M07, 20M35, 20M12

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