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Elementary theory of abelian groups without torsion, with a predicate selecting a subgroup

โœ Scribed by G. T. Kozlov; A. I. Kokorin


Publisher
Springer US
Year
1969
Tongue
English
Weight
564 KB
Volume
8
Category
Article
ISSN
0002-5232

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The Elementary Theory of Torsionfree Abe
โœ Peter H. Schmitt ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 367 KB ๐Ÿ‘ 1 views

This is proved by induction on 7n. For ni = 0 (\*) follows immediately from the definitions. Now take a E C,:,,, for m > 0. There is c E B,,,, such t'hat ac E pCp,n,-l + + C,,;f,l+l. There is thus a' E Cl~.flr-l with a E c + pa' + Cl,.,,f+l. By induction hypothesis a' E 6' + C,.,,, for some b' E @ B