Tight subgroups in torsion-free Abelian groups |
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Authors: | Mohamed A. Ould-Beddi Lutz Strüngmann |
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Affiliation: | (1) Faculté des Sciences et Techniques, Université de Nouakchott, B. P. 5026, Nouakchott, Mauritania;(2) Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, 91904 Jerusalem, Israel |
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Abstract: | LetX be a torsion-free abelian group. We study the class of all completely decomposable subgroups ofX which are maximal with respect to inclusion. These groups are called tight subgroups ofX and we state sufficient conditions on a subgroup to be tight. In particular we consider tight subgroups of bounded completely decomposable groups. For those we show that every regulating subgroup is tight and we characterize the tight subgroups of finite index in almost completely decomposable groups. The second author was supported by a MINERVA fellowship. |
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