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ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS
Published online by Cambridge University Press: 01 January 2009
Abstract
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 c-dimension 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.
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- Copyright © Glasgow Mathematical Journal Trust 2008
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