On extensions of completely simple semigroups by groups

2013/08/14 by Tamás Dékány, Dékány, Tamás
Mathematics · #20M10 #20M17 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #math.GR #math.RA #msc:20M10 #msc:20M17

paper · pdf · doi:10.48550/arxiv.1308.3036

arxiv created 2013/08/14 · arxiv updated 2013/08/15

Abstract

An example of an extension of a completely simple semigroup U by a group H is given which cannot be embedded into the wreath product of U by H. On the other hand, every central extension of U by H is shown to be embeddable in the wreath product of U by H, and any extension of U by H is proved to be embeddable in a semidirect product of a completely simple semigroup V by H where the maximal subgroups of V are direct powers of those of U.

Related

• Normal extensions and full restricted semidirect products of inverse semigroups
• The Direct Extension Theorem
• On extensions of Lie algebras
• Homogeneous completely simple semigroups
• Beyond wreath and block