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Residual Properties of Free Products of Infinitely Many Nilpotent Groups Amalgamating Cycles

✍ Scribed by David Doniz

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 134 KB
Volume: 179
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0045

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✦ Synopsis

We prove that a free product of infinitely many finitely generated, torsion free, nilpotent groups amalgamating isolated cycles is residually finite-p for all primes p so long as the number of generators and nilpotency class of the factors are both bounded. Examples illustrate that if we remove any single hypothesis, the resulting group need not even be residually finite.

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✍ G.S. Kim; J. Mccarron 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 426 KB

We find a necessary and sufficient condition for an amalgamated free product of arbitrarily many isomorphic residually \(p\)-finite groups to be residually \(p\)-finite. We also prove that this condition is sufficient for a free product of any finite number of residually \(p\)-finite groups, amalgam