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Journal Articles Israel Journal of Mathematics Year : 2013

Small, $nm$-stable compact $G$-groups

Krzysztof Krupinski
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Frank Olaf Wagner
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We prove that if $(H,G)$ is a small, $nm$-stable compact $G$-group, then $H$ is nilpotent-by-finite, and if additionally $\NM(H) \leq \omega$, 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 give examples of small, $nm$-stable compact $G$-groups of infinite ordinal $\NM$-rank, providing counter-examples to the $\NM$-gap conjecture.
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Dates and versions

hal-00495141 , version 1 (25-06-2010)
hal-00495141 , version 2 (25-06-2010)
hal-00495141 , version 3 (17-03-2011)
hal-00495141 , version 4 (03-10-2011)



Krzysztof Krupinski, Frank Olaf Wagner. Small, $nm$-stable compact $G$-groups. Israel Journal of Mathematics, 2013, 194 (2), pp.907-933. ⟨10.1007/s11856-012-0103-3⟩. ⟨hal-00495141v4⟩
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