  We use the Bar-Natan Zh-correspondence to identify the generalized Alexander
polynomial of a virtual knot with the Alexander polynomial of a two component
welded link. We show that the Zh-map is functorial under concordance, and also
that Satoh's Tube map (from welded links to ribbon knotted tori in $S^4$) is
functorial under concordance. In addition, we extend classical results of Chen,
Milnor, and Hillman on the lower central series of link groups to links in
thickened surfaces. Our main result is that the generalized Alexander
polynomial vanishes on any knot in a thickened surface which is concordant to a
homologically trivial knot. In particular, this shows that it vanishes on
virtually slice knots. We apply it to complete the calculation of the slice
genus for virtual knots with four crossings and to determine non-sliceness for
a number of 5-crossing and 6-crossing virtual knots.
