Solvability in groups with a chain condition on uniformly definable subgroups

2019/11/05 by Derakhshan, Jamshid
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1911.01589

Abstract

We prove a structure theorem for periodic locally soluble groups satisfying a chain condition on intersections of relatively uniformly definable subgroups using results from the theory of stable groups. The result in particular shows that these groups are soluble, thus giving a model-theoretic and much simpler proof of a special case of a theorem of Bryant and Hartley on the solubility of periodic locally soluble groups satisfying the minimal condition on centralizers.

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