Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

The number of isotype and $ l$-pure subgroups of an abelian $ p$-group


Author: Paul Hill
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20K99

Retrieve articles in all journals with MSC: 20K99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291282-0
Keywords: Abelian p-group, pure subgroups, isotype subgroups, direct sum of countable groups
Article copyright: © Copyright 1972 American Mathematical Society