No Access

On p-Separability of Subgroups of Free Metabelian Groups

Valerij G. Bardakov

Sobolev Institute of Mathematics, Novosibirsk 630090, Russia

https://doi.org/10.1142/S1005386706000253Cited by:2 (Source: Crossref)

Abstract

We prove that every free metabelian non-cyclic group has a finitely generated isolated subgroup which is not separable in the class of nilpotent groups. As a corollary, we prove that for every prime number p, an arbitrary free metabelian non-cyclic group has a finitely generated p′-isolated subgroup which is not p-separable.

The author was supported by RFBR (grant 02-01-01118).

Keywords:

AMSC: 20F16, 20F14, 20F10

References

S. Bachmuth, Trans. Amer. Math. Soc. 118(6), 93 (1965), DOI: 10.2307/1993945. Crossref, Web of Science, Google Scholar
V. G. Bardakov, Siberian Math. J. 45(3), 416 (2004), arXiv: math.GR/0404292 DOI: 10.1023/B:SIMJ.0000028606.51473.f7. Crossref, Web of Science, Google Scholar
M. I. Kargapolov and Yu. I. Merzljakov , Fundamentals of the Theory of Groups ( Springer , New York , 1979 ) . Crossref, Google Scholar
, The Kourovka Notebook Unsolved Problems in Group Theory, 15th edn. (Sobolev Institute of Mathematics, Novosibirsk, 2002). Google Scholar
E. D. Loginova, Sib. Mat. Zh. 40(2), 395 (1999). Google Scholar
R. C. Lyndon and P. E. Schupp , Combinatorial Group Theory , Ergebnisse der Mathematik und ihrer Grenzgebiete ( Springer-Verlag , Berlin-New York , 1977 ) . Crossref, Google Scholar
A. I. Mal'cev, Uchen. Zapiski Ivanovsk. Ped. Instituta 18(5), 49 (1958). Google Scholar
H. Neumann , Varieties of Groups , Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37 ( Springer-Verlag , Berlin-Heidelberg-New York , 1967 ) . Crossref, Google Scholar