Non-algebraic minimal connected simple groups of odd type. (Groupes simples connexes minimaux non-algébriques de type impair.) (French) Zbl 1169.20016
In this paper the author continues the rewriting without the tameness assumption of G. Cherlin and E. Jaligot [J. Algebra 276, No. 1, 13-79 (2004; Zbl 1056.20020)] undertaken in [J. Algebra 317, No. 2, 877-923 (2007; Zbl 1146.20028)]. The first paper of the author concerned the algebraic case, and this second paper is concerned with the (three) configurations of non-algebraic minimal connected simple groups of finite Morley rank of odd type.
In section 2 the structure of the Sylow \(2\)-subgroup is directly limited, which avoids some noise in the argument. The two configurations of Prüfer \(2\)-rank \(1\) are delineated in Section 3. The Prüfer \(2\)-rank \(2\) case is then studied in Sections 4-6; here the concentration argument of the first paper of the author is applied two times, in a very delicate inductive process on the unipotence weight of the three involutions of the Sylow \(2\)-subgroup. In section 7 the conjugacy of involutions is proved, and finally in section 8 the Weyl group is determined by the same kind of techniques as developed by Cherlin and Jaligot [loc. cit.].
In section 2 the structure of the Sylow \(2\)-subgroup is directly limited, which avoids some noise in the argument. The two configurations of Prüfer \(2\)-rank \(1\) are delineated in Section 3. The Prüfer \(2\)-rank \(2\) case is then studied in Sections 4-6; here the concentration argument of the first paper of the author is applied two times, in a very delicate inductive process on the unipotence weight of the three involutions of the Sylow \(2\)-subgroup. In section 7 the conjugacy of involutions is proved, and finally in section 8 the Weyl group is determined by the same kind of techniques as developed by Cherlin and Jaligot [loc. cit.].
Reviewer: Eric Jaligot (Lyon)
MSC:
| 20E32 | Simple groups |
| 03C60 | Model-theoretic algebra |
| 03C45 | Classification theory, stability, and related concepts in model theory |
| 20A15 | Applications of logic to group theory |
| 20E07 | Subgroup theorems; subgroup growth |
References:
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