naa a22 4500 510783414 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0103-3 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0103-3 Small, nm -stable compact G -groups [Elektronische Daten] [Krzysztof Krupiński, Frank Wagner] 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. Hebrew University Magnes Press, 2012 Krupiński Krzysztof Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland aut Wagner Frank CNRS, Institut Camille Jordan UMR 5208 Bâtiment Jean Braconnier, Université de Lyon; Université Lyon 1, 43 boulevard du 11 novembre 1918, F-69622, Villeurbanne-cedex, France aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 194/2(2013-03-01), 907-933 0021-2172 194:2<907 2013 194 11856 https://doi.org/10.1007/s11856-012-0103-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0103-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Krupiński Krzysztof Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland aut NATIONALLICENCE 700 1- Wagner Frank CNRS, Institut Camille Jordan UMR 5208 Bâtiment Jean Braconnier, Université de Lyon; Université Lyon 1, 43 boulevard du 11 novembre 1918, F-69622, Villeurbanne-cedex, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 194/2(2013-03-01), 907-933 0021-2172 194:2<907 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer