On solubility of groups with bounded centralizer chains
نویسندگان
چکیده
The c-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite cdimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch–Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite soluble) group of finite c-dimension k is soluble of derived length bounded in terms of k. 2000 AMS classification. Primary: 20D10; Secondary: 03C20, 20D45, 20F16, 20F22.
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