This article is cited in 5 papers

On the Residual Finiteness of Free Products of Solvable Minimax Groups with Cyclic Amalgamated Subgroups

D. N. Azarov

Ivanovo State University

Abstract: A necessary and sufficient condition for the residual finiteness of a (generalized) free product of two residually finite solvable-by-finite minimax groups with cyclic amalgamated subgroups is obtained. This generalizes the well-known Dyer theorem claiming that every free product of two polycyclic-by-finite groups with cyclic amalgamated subgroups is a residually finite group.

Keywords: residually finite group, (generalized) free product with amalgamated subgroups, polycyclic-by-finite group, minimax group, solvable group, subnormal series, Chernikov group, Fitting subgroup, FATR group.

UDC: 512.543

Received: 17.01.2011

DOI: 10.4213/mzm8971

 English version: Mathematical Notes, 2013, 93:4, 503–509

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