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. 
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     author = {D. I. Moldavanskii},
     title = {The {Intersection} of the {Subgroups} of {Finite} {Index} in {Baumslag--Solitar} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a9/}
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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/