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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The free product of residually finite groups amalgamated along retracts is residually finite


Authors: James Boler and Benny Evans
Journal: Proc. Amer. Math. Soc. 37 (1973), 50-52
MSC: Primary 20E25
DOI: https://doi.org/10.1090/S0002-9939-1973-0306329-3
MathSciNet review: 0306329
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Abstract: It is shown that residual finiteness is preserved by the generalized free product provided that the amalgamated subgroups are retracts of their respective factors. This result is applied to knot groups. The outcome is that the question of residual finiteness for knot groups need only be answered for prime knots.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0306329-3
Keywords: Residually finite group, retract, generalized free product, knot group, prime knot
Article copyright: © Copyright 1973 American Mathematical Society