This article is cited in 12 papers

On the Residual $\pi$-Finiteness of Generalized Free Products of Groups

E. A. Tumanova

Ivanovo State University

Abstract: A criterion for the approximability by finite $\pi$-groups of a generalized free product of two finite $\pi$-groups with normal amalgamated subgroups is obtained. Using this criterion, for a generalized free product of two arbitrary groups with normal amalgamation, we find both necessary and sufficient conditions for the residual $\pi$-finiteness that are similar to the Baumslag conditions for the property of residual finiteness. Some applications of this result are indicated.

Keywords: residual finiteness, residual $\pi$-finiteness, generalized free product with normal amalgamation, approximability by finite $\pi$-groups.

UDC: 512.543

Received: 05.10.2012
Revised: 11.06.2013

DOI: 10.4213/mzm10210

 English version: Mathematical Notes, 2014, 95:4, 544–551

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