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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The number of isotype and $l$-pure subgroups of an abelian $p$-group
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by Paul Hill PDF
Proc. Amer. Math. Soc. 32 (1972), 69-74 Request permission

Abstract:

The number of isotype subgroups of an abelian p-group G is determined. This solves a recent problem of Fuchs. Actually, we accomplish slightly more. Define a subgroup H of an abelian p-group G to be an l-pure subgroup of G if, for some ordinal $\lambda$, H is ${p^\lambda }$-pure in G and ${p^\lambda }H$ is divisible. We compute the number of l-pure subgroups of G and show that the number of l-pure subgroups and the number of isotype subgroups of G coincide. Our final result deals with the number of nonisomorphic isotype subgroups of G when G is a direct sum of countable groups.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 32 (1972), 69-74
  • MSC: Primary 20K99
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0291282-0
  • MathSciNet review: 0291282