Geodesic
On the Residual Finiteness of Free Products of Solvable Minimax Groups with Cyclic Amalgamated Subgroups
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 483-491

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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, subnormal series, Fitting subgroup, FATR group.
Mots-clés : solvable group, Chernikov group 
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     author = {D. N. Azarov},
     title = {On the {Residual} {Finiteness} of {Free} {Products} of {Solvable} {Minimax} {Groups} with {Cyclic} {Amalgamated} {Subgroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--491},
     publisher = {mathdoc},
     volume = {93},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a0/}
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D. N. Azarov. On the Residual Finiteness of Free Products of Solvable Minimax Groups with Cyclic Amalgamated Subgroups. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 483-491. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a0/