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This short note reviews the main contributions of the Ph.D. thesisof Imre Simon.His graduate work had major impact on algebraic theory of automataand thirty years later we are in a good position to appreciatehow sensitive he was in selecting good problems, and how clever insolving them!
We find the atoms of certain subclasses of varieties of finite semigroups and the corresponding varieties of languages. For example we give a new description of languages whose syntactic monoids are R-trivial and idempotent. We also describe the least variety containing all commutative semigroups and at least one non-commutative semigroup. Finally we extend to varieties of finite semigroups some classical results about semilattice decomposition of semigroups.
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