Small, nm-stable compact G-groups |
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| Authors: | Krzysztof Krupiński Frank Wagner |
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| Institution: | 1103. Instytut Matematyczny, Uniwersytet Wroc?awski, pl. Grunwaldzki 2/4, 50-384, Wroc?aw, Poland
2103. CNRS, Institut Camille Jordan UMR 5208 Batiment Jean Braconnier, Université de Lyon; Université Lyon 1, 43 boulevard du 11 novembre 1918, F-69622, Villeurbanne-cedex, France
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| Abstract: | 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 or NM(H) = ω α for some ordinal α, then H is abelian-by-finite. 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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