Journal of Symbolic Logic

On the definability of radicals in supersimple groups

Cé{d}ric Milliet

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Abstract

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

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

Dates
First available in Project Euclid: 15 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1368627069

Digital Object Identifier
doi:10.2178/jsl.7802160

Mathematical Reviews number (MathSciNet)
MR3145200

Zentralblatt MATH identifier
1314.03036

Subjects
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]

Keywords
Supersimple group Fitting subgorup soluble radical

Citation

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. https://projecteuclid.org/euclid.jsl/1368627069


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