Open AccessOn the definability of radicals in supersimple groups
Author(s) -
Cédric Milliet
Publication year - 2013
Publication title -
journal of symbolic logic
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.831
H-Index - 47
eISSN - 1943-5886
pISSN - 0022-4812
DOI - 10.2178/jsl.7802160
Subject(s) - nilpotent , rank (graph theory) , mathematics , normal subgroup , group (periodic table) , nilpotent group , pure mathematics , combinatorics , fitting subgroup , characteristic subgroup , chemistry , organic chemistry
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
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