On the Approximability by Finite p-Groups of Free Products of Groups with Normal Amalgamation |
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Authors: | E V Sokolov |
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Institution: | (1) Ivanovo State University, Ivanovo, Russia |
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Abstract: | A sufficient condition for the residual p-finiteness (approximability by the class
of finite p-groups) of a free product G = (A * B; H) of groups A and B with a normal amalgamated subgroup H is obtained. This condition is used to prove that if A and B are extensions of residually
-groups by
-groups, where
stands for the class of finitely generated torsion-free nilpotent groups, and if H is a normal p′-isolated polycyclic subgroup, then the group G is residually p-finite (i.e., residually
-group), provided the quotient group G/H
p
H′ is residually p-finite.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 125–131.Original Russian Text Copyright © 2005 by E. V. Sokolov. |
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Keywords: | residually p-finite amalgamated subgroup normal amalgamated subgroup isolated subgroup polycyclic group |
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