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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.