We are using Oprah's discussion guide to help facilitate the dialog. the recap below is from her website.
Part Four: Marriage and Divorce Laws
Many contemporary readers picking up Anna Karenina for the first time ask a very logical question after the consummation of Anna and Vronsky's affair: Why don't Anna and Karenin simply divorce? It would seem to solve many of the messiest issues for the three lovers in this triangle. Though that may seem to "solve" the problem, when thinking it through, the truth is that divorce in Tolstoy's Russia produced another set of complications potentially more devastating. All legal issues aside, Karenin and Anna feel the sacredness of their union in their own ways. This is part of the reason for Anna's extreme guilt and Karenin's extreme confusion.