The Free Product of Two Groups with a Malnormal Amalgamated Subgroup
- 1 October 1971
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 23 (5) , 933-959
- https://doi.org/10.4153/cjm-1971-102-8
Abstract
In [1], B. Baumslag defined a subgroup U of a group G to be malnormal in G if gug–1 ∈ U, 1 ≠ u ∈ U, implies that g ∈ U. 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 u ∈ U. 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.Keywords
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