A torsion-free abelian group of finite rank exists whose quotient group modulo the square subgroup is not a nil-group |
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Authors: | RR Andruszkiewicz |
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Institution: | Institute of Mathematics, University of Bia?ystok, 15-245 Bia-lystok, K. Cio-lkowskiego 1M, Poland |
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Abstract: | The first example of a finite rank torsion-free abelian group A such that the quotient group of A modulo the square subgroup of A is not a nil-group is indicated (in both cases of associative and general rings). In particular, the answer to the question posed by A.E. Stratton and M.C. Webb in 18], Abelian groups, nil modulo a subgroup, need not have nil quotient group, Publ. Math. Debrecen. 27 (1980), 127–130, is given for finite rank torsion-free groups. A relationship between nontrivial p-pure subgroups of the additive group of p-adic integers and nontrivial ? p?1]-submodules of the field of p-adic numbers is investigated. In particular, a bijective correspondence between these structures is proven using only elementary methods. |
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Keywords: | Primary 20K99 Secondary 13A15 |
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