Redidual properties in supersimple groups. (Propriétés résiduelles dans les groupes supersimples.) (French. English summary) Zbl 1222.03038

Let \(C\) be a pseudo-variety, that is, a class of groups closed under subgroups, factor groups and finite products. Call a group \(G\) residually \(C\) if, for every element \(g \neq 1_G\) of \(G\), there is a normal subgroup \(N\) of \(G\) such that \(G/N \in C\) and \(g \not \in N\). The author shows that, if \(G\) is a supersimple residually \(C\) group, then there is a normal series of definable subgroups of \(G\), \(G = G_0 \supseteq G_1 \supseteq \ldots \supseteq G_n\), such that, for every \(i < n\), \(G_i/G_{i+1} \in C\) and \(G_n\) is nilpotent. This extends in the semisimple setting and strenghtens previous results by Ould Houcine for superstable residually \(C\) groups.


03C45 Classification theory, stability, and related concepts in model theory
20A15 Applications of logic to group theory
20E26 Residual properties and generalizations; residually finite groups
Full Text: DOI


[1] Simple theories (2000)
[2] DOI: 10.1002/malq.200610023 · Zbl 1109.03028 · doi:10.1002/malq.200610023
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