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Characterizations of Warfield Groups

โœ Scribed by Peter Loth

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
153 KB
Volume
204
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Warfield groups are defined to be direct summands of simply presented abelian groups. By introducing a global definition of quasi-sequentially nice subgroups we prove some characterizations of Warfield groups involving these groups, knice subgroups, and valuated coproducts. Furthermore, we exhibit a new proof of a characterization of Warfield groups in terms of nice subgroups and valuated coproducts.

๐Ÿ“œ SIMILAR VOLUMES

The Transitivity of Local Warfield Group
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โœ Paul Hill; William Ullery ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 234 KB

For a fixed prime p, let G denote a module over the integers localized at p. ลฝ . Such a module is often referred to as a p-local abelian group. Following established precedent, we say that G is transitive provided that there exists an automorphism of G that maps a onto b whenever a and b are element

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when A is a torsion-free abelian group of rank one. As a consequence he was able to show that a finite rank torsion-free group M satisfies M ( nat M\*\* if and only if M F A I and pM s M precisely when pA s A, where ลฝ . M\*sHom y, A . Using this Warfield obtained a characterization of Z ลฝ . w x the