Sufficient conditions are provided for A∪S-separability of subgroups in free products of a free group and a LERF group, with the corollary that finitely generated infinite-index subgroups of free groups are A∪S-separable in such products.
Mal’cev,On homomorphisms onto finite groups, Ivanov
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Alternating and Symmetric Separability of Free Products
Sufficient conditions are provided for A∪S-separability of subgroups in free products of a free group and a LERF group, with the corollary that finitely generated infinite-index subgroups of free groups are A∪S-separable in such products.