On Preservation of Stability for Finite Extensions of Abelian Groups | Zendy

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On Preservation of Stability for Finite Extensions of Abelian Groups

Author(s) -

Haug Frieder

Publication year - 1994

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19940400103

Subject(s) - abelian group , mathematics , sylow theorems , conjugacy class , locally finite group , rank of an abelian group , elementary abelian group , mathematics subject classification , pure mathematics , torsion subgroup , ca group , solvable group , finite group , group (periodic table) , chemistry , organic chemistry

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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