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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Amalgamated products of profinite groups: Counterexamples


Author: Luis Ribes
Journal: Proc. Amer. Math. Soc. 37 (1973), 413-416
MSC: Primary 20F20
MathSciNet review: 0382463
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Abstract: If $ {A_1}$ and $ {A_2}$ are profinite groups with a common closed subgroup H, the profinite amalgamated product of $ {A_1}$ and $ {A_2}$ over H is said to exist if $ {A_1}$ and $ {A_2}$ are canonically embedded in the push-out of $ {A_1}$ and $ {A_2}$ over H in the category of profinite groups. It is proved that such products need not exist.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0382463-7
PII: S 0002-9939(1973)0382463-7
Keywords: Profinite group, pro-p-group, amalgamated product, push-out, nilpotent group
Article copyright: © Copyright 1973 American Mathematical Society