Summary
We show that a stable groupG satisfying certain commutator conditions is nilpotent. Furthermore, a soluble stable group with generically splitting automorphism of prime order is nilpotent-by-finite. In particular, a soluble stable group with a generic element of prime order is nilpotent-by-finite.
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The author would like to thank Ali Nesin for pointing out an error in an earlier version of this paper and various valuable comments
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Wagner, F.O. Commutator conditions and splitting automorphisms for stable groups. Arch Math Logic 32, 223–228 (1993). https://doi.org/10.1007/BF01375553
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DOI: https://doi.org/10.1007/BF01375553