Abstract

The relations of almost containedness and orthogonality in the lattice of groups of finitary permutations are studied in the paper. We define six cardinal numbers naturally corresponding to these relations by the standard scheme of P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P$$\end{document}. We obtain some consistency results concerning these numbers and some versions of the Ramsey theorem.