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Glasgow Mathematical Journal (1)

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ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS
E. I. KHUKHRO
Journal:

Glasgow Mathematical Journal / Volume 51 / Issue 1 / January 2009

Published online by Cambridge University Press:

01 January 2009, pp. 49-54

Print publication:

January 2009
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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.