The Free Product of Two Groups with a Malnormal Amalgamated Subgroup

Abstract
In [1], B. Baumslag defined a subgroup U of a group G to be malnormal in G if gug–1U, 1 ≠ uU, implies that gU. Baumslag considered the class of amalgamated products (A * B; U) in which U is malnormal in both A and B. These amalgamated products play an important role in the investigations of B. B. Newman [13] of groups with one defining relation having torsion. In this paper, we shall be concerned primarily with a generalization of this class.Let U be a subgroup of a group G and let uU. Then the extended normalizer EG(u, U) of u relative to U in G is defined by if u ≠ 1, and by EG(u, U) = U if u = 1.

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