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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{MZM_2013_93_4_a0,
     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/}
}
TY  - JOUR
AU  - D. N. Azarov
TI  - On the Residual Finiteness of Free Products of Solvable Minimax Groups with Cyclic Amalgamated Subgroups
JO  - Matematičeskie zametki
PY  - 2013
SP  - 483
EP  - 491
VL  - 93
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a0/
LA  - ru
ID  - MZM_2013_93_4_a0
ER  - 
%0 Journal Article
%A D. N. Azarov
%T On the Residual Finiteness of Free Products of Solvable Minimax Groups with Cyclic Amalgamated Subgroups
%J Matematičeskie zametki
%D 2013
%P 483-491
%V 93
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a0/
%G ru
%F MZM_2013_93_4_a0
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/

[1] G. Baumslag, “On the residual finiteness of generalized free products of nilpotent groups”, Trans. Amer. Math. Soc., 106 (1963), 193–209 | DOI | MR | Zbl

[2] J. L. Dyer, “On the residual finiteness of generalized free products”, Trans. Amer. Math. Soc., 133 (1968), 131–143 | DOI | MR | Zbl

[3] J. Lennox, D. J. Robinson, The Theory of Infinite Soluble Groups, Oxford Math. Monogr., The Clarendon Press, Oxford, 2004 | MR | Zbl

[4] G. Baumslag, D. Solitar, “Some two-generator one-relator non-Hopfian groups”, Bull. Amer. Math. Soc., 68 (1962), 199–201 | DOI | MR | Zbl

[5] A. I. Maltsev, “O gomomorfizmakh na konechnye gruppy”, Uchen. zap. Ivanovsk. ped. in-ta, 18:5 (1958), 49–60

[6] K. A. Hirsch, “On infinite soluble groups (IV)”, J. London Math. Soc., 27 (1952), 81–85 | DOI | MR | Zbl

[7] M. Shirvani, “A convers to a residual finiteness theorem of G. Baumslag”, Proc. Amer. Math. Soc., 104:3 (1988), 703–706 | DOI | MR | Zbl