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One-relator products of torsion-free groups

Published online by Cambridge University Press:  18 May 2009

S. D. Brodskiĭ  and
James Howie
S. D. Brodskiĭ
Affiliation:
Department of MathematicsAfula Research Institute Afula, Israel Department of MathematicsHeriot-Watt University Riccarton Edinburgh, EH14 4AS
James Howie
Affiliation:
Department of MathematicsAfula Research Institute Afula, Israel Department of MathematicsHeriot-Watt University Riccarton Edinburgh, EH14 4AS
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If A and B are torsion-free groups, and W is a cyclically reduced word of even length in A*B, it is generally conjectured that a Freiheitssatz holds, namely that each of A and B are embedded via the natural map into the one-relator product group G = (A*B)/N(W), where N denotes normal closure. If W has length 2, then G is a free product of A and B with infinite cyclic amalgamation, and the result is obvious. The purpose of this note is to prove the Freiheitssatz in some special cases.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 1 , January 1993 , pp. 99 - 104
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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