Geodesic
The Intersection of the Subgroups of Finite Index in Baumslag–Solitar Groups
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 92-100

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For any one-relator group in the family of Baumslag–Solitar groups, a system of its elements is indicated whose normal closure in the group coincides with the intersection of all normal finite-index subgroups. The well-known criterion for the residual finiteness of Baumslag–Solitar groups is an immediate consequence of this result. It is also shown that, if the intersection of all finite-index normal subgroups in a Baumslag–Solitar group differs from the identity subgroup (i.e., if the group is not residually finite), then this intersection cannot be the normal closure of any finite set of elements.
Keywords: Baumslag–Solitar group, finite-index subgroup, one-relator group, residual finiteness, normal closure, amalgamated product. 
D. I. Moldavanskii. The Intersection of the Subgroups of Finite Index in Baumslag–Solitar Groups. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 92-100. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a9/
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