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On a class of torsion-free abelian groups of finite rank. (English. Russian original) Zbl 0833.20064
Math. Notes 55, No. 6, 589-595 (1994); translation from Mat. Zametki 55, No. 6, 74-72 (1994).
A class of torsion free finite rank Abelian groups is characterized in this paper. The class can be treated as a generalization of Murley’s $$\mathcal E$$-group class. The results of A. Fomin’s paper [Algebra Logika 26, No. 1, 63-83 (1987; Zbl 0638.20030)] are applied.

##### MSC:
 20K15 Torsion-free groups, finite rank
##### Keywords:
finite rank Abelian groups; $$\mathcal E$$-groups
Zbl 0638.20030
Full Text:
##### References:
 [1] C. E. Murley, ”The classification of certain classes of torsion-free Abelian groups,”Pacific. J. Math.,40, No. 3, 647–665 (1972). · Zbl 0261.20045 [2] F. Richman, ”A class of rank 2 torsion-free groups,” In:Studies on Abelian Groups, Paris (1968), pp. 327–333. · Zbl 0182.04103 [3] R. B. Worfild, ”Homomorphisms and duality for torsion-free groups,”Math. Z.,107, 189–200 (1968). · Zbl 0169.03602 [4] A. A. Fomin, ”Duality in some classes of torsion-free Abelian groups of finite rank,”Sib. Mat. Zh.,36, 117–127 (1986). · Zbl 0633.20031 [5] D. W. Dubois, ”Cohesive groups and p-adic integers,”Publ. Math. Debrecen.,12, No. 1, 51–58 (1965). · Zbl 0136.29002 [6] A. A. Fomin, ”Abelian groups with one r-adic relation,”Algebra Logika,28, No. 1, 83–104 (1989). · Zbl 0692.20019 [7] D. M. Arnold, ”A duality for quotient divisible Abelian groups of finite rank,”Pacific J. Math.,5, No. 1, 61–98 (1961). [8] L. Fuks,Infinite Abelian Groups, Vol. 1, Mir, Moscow (1974). [9] A. A. Fomin, ”Invariants and duality in some classes of torsion-free Abelian groups of finite rank,”Algebra Logika,1, 63–83 (1987). · Zbl 0638.20030
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