Join Irreducible Pseudovarieties, Group Mapping, and Kovács-Newman Semigroups

  • John Rhodes
  • Benjamin Steinberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


We call a pseudovariety finite join irreducible if

\(V\leq V_{1}v V_{2}\Longrightarrow V \leq V_{1} {\rm or} V \leq V_{2}. \)

We present a large class of group mapping semigroups generating finite join irreducible pseudovarieties. We show that many naturally occurring pseudovarieties are finite join irreducible including: S, DS, CR, CS and \(\overline{H}\), where H is a group pseudovariety containing a non-nilpotent group.


Normal Subgroup Maximal Subgroup Nilpotent Group Group Mapping Minimal Normal Subgroup 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • John Rhodes
    • 1
  • Benjamin Steinberg
    • 2
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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