id: 05313068
dt: j
an: 05313068
au: Bridson, Martin R.; Wilton, Henry
ti: Subgroup separability in residually free groups.
so: Math. Z. 260, No. 1, 25-30 (2008).
py: 2008
pu: Springer-Verlag, Berlin
la: EN
cc: 
ut: residually free groups; finitely presented subgroups; virtual retracts;
    subgroups of finite index; membership problem
ci: 
li: doi:10.1007/s00209-007-0256-7
ab: A group $G$ is called residually free if, given an element $g\in G\setminus
    1$, there exists a homomorphism $f\colon G\to F$ ($F$ free) with
    $f(g)\ne 1$. It is proved that the finitely presentable subgroups of
    residually free groups are separable and that the subgroups of type
    $\text{FP}_\infty$ over ${\bbfQ}$ are virtual retracts. Remind that a
    subgroup $H$ of a group $G$ is a virtual retract if and only if it is
    contained in a subgroup $V$ of $G$ of finite index for which $H$ is a
    retract. A uniform solution to the membership problem for finitely
    presentable subgroups of residually free groups is given.
rv: V. A. Roman’kov (Omsk)