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The Free Product of Two Groups with a Malnormal Amalgamated Subgroup

Published online by Cambridge University Press:  20 November 2018

A. Karrass  and
D. Solitar
A. Karrass
Affiliation:
York University, Toronto, Ontario
D. Solitar
Affiliation:
York University, Toronto, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 5 , October 1971 , pp. 933 - 959
Copyright
Copyright © Canadian Mathematical Society 1971

Footnotes

This research was supported by NRC Grants A5614 and A5602.

References

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