Proceedings of the American Mathematical Society

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

 

 

A lemma on extensions of abelian groups


Author: Adolf Mader
Journal: Proc. Amer. Math. Soc. 78 (1980), 304-306
MSC: Primary 20K35; Secondary 20E22
MathSciNet review: 553362
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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 $ \vert{G_2}\vert \leqslant \vert G/H\vert \cdot {\aleph _0}$. There are a variety of applications.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0553362-6
Keywords: Fuchs 5 group, extension, summand
Article copyright: © Copyright 1980 American Mathematical Society