Abstract
The class of pure subgroups of completely decomposable groups of finite rank was introduced and investigated by Butler in [5]. Lady called the groups in this class “Butler groups”. Some other authors studied Butler groups under different names (see Koehler [9] and the first author [3] and [4]). Recently, Arnold collected the known results on Butler groups in [1], and investigated more deeply this class of finite rank groups.
Keywords
- Abelian Group
- Exact Sequence
- Finite Rank
- Torsion Group
- Pure Subgroup
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work was done while the first author was visiting professor at the University of Padova, Italy, supported by the Italian C.N.R.
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References
ARNOLD, D.M. “Pure subgroups of finite rank completely decomposable groups” Proc.Oberwolfach,Lecture Notes n.874, pgg.1–31. Springer Verlag,Berlin, 1981.
BICAN, L. “Taxed abelian groups of torsion-free rank one” Czech. Math.J. 20 (95) 232–242 (1970).
BICAN, L. “Purely finitely generated abelian groups” Comment.Math. Univ.Carolinae 10) 1–81 (197.
BICAN, L. “Splitting in abelian groups” Czech.TJlath.J. 28 (103) 356–364 (1978).
BUTLER, M.C.R. “A class of torsion-free abelian groups of finite rank” Proc.London Ma.th.Soc. 15 680–698 (1965).
FUCHS, L. “Infinite Abelian Groups” Vol.I and II, Academic Press London, New York, 1971 and 1973.
GRIFFITH, P. “A solution to the splitting mixed group problem of Baer” Trans.Amer.Math.Soc. 139 261–270 (1969).
HUNTER, R.H. “Balanced sequences of abelian groups” Trans.Amer. Math.Soc. 215 81–98 (1976).
KOEHLER, J. “The type set of a torsion-free group of finite rank” Illinois J.Math. 9 66–86 (1965).
LADY, L. “Extensions of scalars for torsion-free modules over Dedekind domains” Symposia Math. 23 287–305 (1979).
MACLANE, S. “Homology” Springer Verlag, Berlin, 1963.
PROCHÂZKA, L. “Sur p-inépendance et p -indépendance en des groupes sans torsion” Symposia Math. 23 107–120 (1979).
PROCHÂZKA, L. “14w-basic subgroups of torsion-free abelian groups” Proc.Oberwolfach,Lecture Notes n.874, pgg.127–153. Springer Verlag, Berlin 1981.
SKLYARENKO, E.G. “Relative homological algebra in categories of modules” Russian Math.Surveys 33, 97–137 (1978).
WALKER, C.P. “Relative homological algebra and abelian groups” Illinois J.Math. 10 186–209 (1966).
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© 1983 Springer-Verlag Berlin Heidelberg
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Bican, L., Salce, L. (1983). Butler Groups of Infinite Rank. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_6
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DOI: https://doi.org/10.1007/978-3-662-21560-9_6
Publisher Name: Springer, Berlin, Heidelberg
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