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The Elementary Theory of Torsionfree Abelian Groups With a Predicate Specifying a Subgroup

โœ Scribed by Peter H. Schmitt

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
367 KB
Volume
28
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 @ BP>,,. Thus a E (c + pb') + C I ~, l l l + l . O ~I i < . a L e m m a 7 . With. respect to the topology iiidtcced 1x7. El, by the p-adic topology on. A , B,, i s complete and Hausdorff .

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