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On Amalgamated Free Products of Residually p-Finite Groups

โœ Scribed by G.S. Kim; J. Mccarron

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
426 KB
Volume
162
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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, amalgamating a cyclic subgroup, to be residually (p)-finite. We observe that a group is potent, if it is residually (p)-finite, for all primes (p). Using this fact, we prove that a free product of finitely many groups, amalgamating a maximal cyclic subgroup is potent, if each factor is either free or finitely generated, torsion-free, and nilpotent. ' 1993 Academic Press. Inc.

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