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.References
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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