Is there a residually nilpotent one-relator group that is not residually a finite p-group for any prime p? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T12:51:44Z http://mathoverflow.net/feeds/question/77845 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77845/is-there-a-residually-nilpotent-one-relator-group-that-is-not-residually-a-finite Is there a residually nilpotent one-relator group that is not residually a finite p-group for any prime p? James 2011-10-11T18:20:16Z 2011-10-11T20:52:27Z <p>This question is not directly related to, but was inspired by, <a href="http://mathoverflow.net/questions/77583/is-the-free-product-of-arbitrarily-many-copies-of-mathbbz-and-mathbb" rel="nofollow">this question</a>. We know that a finitely generated residually nilpotent group is residually of prime-power order. However, we may need to use different primes for different elements. Classes of groups for which residual nilpotence forces there to be a single prime that will do for all elements (i.e., for which the group in question must be residually \$p\$-finite, for some \$p\$) seem to be interesting, and include, for instance, free products of cyclic groups.</p> <p><b>Is there a (non-cyclic) one-relator group that is residually nilpotent, but is not residually a finite \$p\$-group, for any prime number \$p\$?</b></p> <p>Such a group must be torsion-free, with trivial centre.</p>