Completely regular semigroups CR\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {C}\mathcal {R}$$\end{document} are unions of their subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by L(CR)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {L}(\mathcal {C}\mathcal {R})$$\end{document}. The Polák theorem concerns the computation of joins in L(CR)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {L}(\mathcal {C}\mathcal {R})$$\end{document}. The B\documentclass[12pt]{minimal}
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\begin{document}$$\mathbf {B}$$\end{document}-relation on L(CR)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {L}(\mathcal {C}\mathcal {R})$$\end{document} identifies varieties with the same bands. We elaborate upon two nontrivial conditions in Polák’s theorem applied to certain subsets of CR\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {C}\mathcal {R}$$\end{document} which amounts to solving particular equations in L(CR)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {L}(\mathcal {C}\mathcal {R})$$\end{document}.
