Small, nm-stable compact G-groups
نویسندگان
چکیده
We prove that if (H,G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) ≤ ω, then H is abelian-byfinite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank.
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