The Bender method in groups of finite Morley rank

Details The Bender method in groups of finite Morley rank The Bender method in groups of finite Morley rank

2007-11-27

arxiv.org/abs/0711.4152v1

J. Algebra 307 (2007) 704--726

Mathematics

Group Theory

Scientific paper

Jaligot's Lemma states that the Fitting subgroups of distinct Borel subgroups do not intersect in a tame minimal simple groups of finite Morley. Such a strong result appears hopeless without tameness. Here we use the 0-unipotence theory to build a toolkit for the analysis of nonabelian intersections of Borel subgroups. As a demonstration, we show that any connected nilpotent subgroup of an intersection of Borel subgroups, in a nontame minimal simple group, must actually be abelian.

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