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The theory of Abelian groups with predicates specifying a subgroup, and with endomorphism operations

✍ Scribed by V. I. Mart'yanov

Publisher: Springer US
Year: 1975
Tongue: English
Weight: 403 KB
Volume: 14
Category: Article
ISSN: 0002-5232
DOI: 10.1007/bf01668811

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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

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