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19.101 (2018)

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The maximum length of a chain of nested centralizers of a group is called its c-dimension. Let $G$ be a locally finite group of finite c-dimension $k$, and let $S$ be the preimage in $G$ of the socle of $G/R$, where $R$ is the locally solvable radical of $G$. Is it true that the factor group $G/S$ contains an abelian subgroup of index bounded by a function of $k$?

Contributor: A. V. Vasil'ev

Progress

Yes, it is true (A. A. Buturlakin, J. Algebra Appl., 18, no. 12 (2019), 1950223, 12 pp).

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