Abstract
This paper enriches the list of properties of the congruence sequences starting from the universal relation and successively performing the operations of lower t and lower k. Three classes of completely regular semigroups, namely semigroups for which is a cryptogroup, semigroups for which is a cryptogroup and semigroups for which κ is over rectangular bands, are studied. and are found to be the least congruences on S such that the quotient semigroups are semigroups for which is a cryptogroup, is a cryptogroup and κ is over rectangular bands, respectively. The results obtained present a response to three problems in Petrich and Reilly’s textbook “Completely Regular Semigroups”.
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