Mathematical Logic Quarterly

On Preservation of Stability for Finite Extensions of Abelian Groups

Journal Article

Abstract

We characterize preservation of superstability and ω‐stability for finite extensions of abelian groups and reduce the general case to the case of p‐groups. In particular we study finite extensions of divisible abelian groups. We prove that superstable abelian‐by‐finite groups have only finitely many conjugacy classes of Sylow p‐subgroups.

Mathematics Subject Classification: 03C60, 20C05.

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