Torsion in Profinite Completions of Torsion-free Groups
نویسنده
چکیده
LET G be a residually-finite torsion-free group. Is Gthe profinite completion of G-torsion free? This question was asked in [CKL] where it was shown that if G is a finitely generated metabelian-by-finite group then indeed G is torsion free. On the other hand Evans [E] showed that if G is not finitely generated then it is possible that G has torsion. His example is also metabelian. In this note we observe that G might have torsion even if G is finitely generated (but of course not metabelian in light of [CKL]). In fact we present an example of a finitely generated torsion free group whose pro-finite completion contains as much torsion as one can wish.
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