Journal of Symbolic Logic

On the definability of radicals in supersimple groups

Cé{d}ric Milliet

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If $G$ is a group with a supersimple theory having a finite $SU$-rank, then the subgroup of $G$ generated by all of its normal nilpotent subgroups is definable and nilpotent. This answers a question asked by Elwes, Jaligot, Macpherson and Ryten. If $H$ is any group with a supersimple theory, then the subgroup of $H$ generated by all of its normal soluble subgroups is definable and soluble.

Article information

J. Symbolic Logic, Volume 78, Issue 2 (2013), 649-656.

First available in Project Euclid: 15 May 2013

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C45: Classification theory, stability and related concepts [See also 03C48] 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
Secondary: 20F16: Solvable groups, supersolvable groups [See also 20D10] 20F18: Nilpotent groups [See also 20D15]

Supersimple group Fitting subgorup soluble radical


Milliet, Cé{d}ric. On the definability of radicals in supersimple groups. J. Symbolic Logic 78 (2013), no. 2, 649--656. doi:10.2178/jsl.7802160.

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