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

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

2010-06-26

arxiv.org/abs/1006.5139v3

Mathematics

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Scientific paper

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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