Let LF be the lattice of all subgroups of the group \(SF(\omega )\) of all finitary permutations of the set of natural numbers. We consider subgroups of \(SF(\omega )\) of the form \(C\cap SF(\omega )\), where C is a compact subgroup of the group of all permutations. In particular, we study their distribution among elements of LF. We measure this using natural relations of orthogonality and almost containedness. We also study complexity of the corresponding families of compact subgroups of \(S(\omega )\).

中文翻译：

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$$ S（\ omega）$$ S（ω）的紧致子组的最终阴影

令LF为自然数集的所有最终置换的\（SF（\ omega）\）组的所有子组的晶格。我们考虑的子组\（SF（\欧米加）\）的形式的\（C \帽SF（\欧米加）\） ，其中Ç是该组的所有排列的紧凑子组。特别是，我们研究了它们在LF元素之间的分布。我们使用正交性和几乎包含性的自然关系来衡量这一点。我们还研究了\（S（\ omega）\）的紧致子组的相应族的复杂性。