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HOMOGENEOUS COMPLETELY SIMPLE SEMIGROUPS
Author(s) -
QuinnGregson Thomas
Publication year - 2020
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12035
Subject(s) - mathematics , simple (philosophy) , semigroup , homogeneous , krohn–rhodes theory , special classes of semigroups , isomorphism (crystallography) , automorphism , idempotence , classification of finite simple groups , modulo , simple group , pure mathematics , discrete mathematics , combinatorics , group of lie type , group theory , crystallography , philosophy , crystal structure , chemistry , epistemology
A semigroup is completely simple if it has no proper ideals and contains a primitive idempotent. We say that a completely simple semigroup S is a homogeneous completely simple semigroup if any isomorphism between finitely generated completely simple sub‐semigroups of S extends to an automorphism of S . Motivated by the study of homogeneous completely regular semigroups, we obtain a complete classification of homogeneous completely simple semigroups, modulo the group case. As a consequence, all finite regular homogeneous semigroups are described, thus extending the work of Cherlin on homogeneous finite groups.

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