On the definability of radicals in supersimple groups

Cédric Milliet (1, 2)

1 ICJ - Institut Camille Jordan
2 Département de Mathématiques

If G is a group with supersimple theory having finite SU-rank, 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 a group with supersimple theory, the subgroup of H generated by all of its normal soluble subgroups is definable and soluble.

Mots clés: Model theory; supersimple group; Fitting subgroup; soluble radical

Domaines: Logique [math.LO]

Cédric Milliet. On the definability of radicals in supersimple groups. The Journal of Symbolic Logic, 2013, 78 (2), pp.649-656. ⟨10.2178/jsl.7802160⟩. ⟨hal-00680001v2⟩