A lemma on extensions of abelian groups
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- by Adolf Mader PDF
- Proc. Amer. Math. Soc. 78 (1980), 304-306 Request permission
Abstract:
We prove: If H is a Fuchs 5 group, then for all groups G containing H it follows that $H = {H_1} \oplus {H_2},G = {H_1} \oplus {G_2}$ such that ${H_2} \subset {G_2}$ and $|{G_2}| \leqslant |G/H| \cdot {\aleph _0}$. There are a variety of applications.References
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- John M. Irwin and Fred Richman, Direct sums of countable groups and related concepts, J. Algebra 2 (1965), 443–450. MR 191955, DOI 10.1016/0021-8693(65)90005-0
- A. Richard Mitchell and Roger W. Mitchell, Some structure theorems for infinite Abelian $P$-groups, J. Algebra 5 (1967), 367–372. MR 204519, DOI 10.1016/0021-8693(67)90047-6
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 304-306
- MSC: Primary 20K35; Secondary 20E22
- DOI: https://doi.org/10.1090/S0002-9939-1980-0553362-6
- MathSciNet review: 553362