Necessary conditions of the approximability of generalized free products and
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2017), pp. 36-47.

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

We obtain a generalization of Shirvani results on necessary conditions of the residual finiteness of generalized free products and HNN-extensions for the case of the property "to be residually a $\mathcal{C}$-group", where $\mathcal{C}$ is an arbitrary class of groups.
Keywords: residual properties, free product of groups with one amalgamated subgroup, multiple HNN-extension.
@article{IVM_2017_9_a3,
     author = {A. E. Kuvaev and E. V. Sokolov},
     title = {Necessary conditions of the approximability of generalized free products and},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {36--47},
     publisher = {mathdoc},
     number = {9},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_9_a3/}
}
TY  - JOUR
AU  - A. E. Kuvaev
AU  - E. V. Sokolov
TI  - Necessary conditions of the approximability of generalized free products and
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 36
EP  - 47
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_9_a3/
LA  - ru
ID  - IVM_2017_9_a3
ER  - 
%0 Journal Article
%A A. E. Kuvaev
%A E. V. Sokolov
%T Necessary conditions of the approximability of generalized free products and
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 36-47
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_9_a3/
%G ru
%F IVM_2017_9_a3
A. E. Kuvaev; E. V. Sokolov. Necessary conditions of the approximability of generalized free products and. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2017), pp. 36-47. http://geodesic.mathdoc.fr/item/IVM_2017_9_a3/

[1] Baumslag G., “On the residual finiteness of generalized free products of nilpotent groups”, Trans. Amer. Math. Soc., 106:2 (1963), 193–209 | DOI | MR | Zbl

[2] Baumslag B., Tretkoff M., “Residually finite HNN-extensions”, Comm. Algebra, 6:2 (1978), 179–194 | DOI | MR | Zbl

[3] Loginova E.D., “Finitnaya approksimiruemost svobodnogo proizvedeniya dvukh grupp s kommutiruyuschimi podgruppami”, Sib. matem. zhurn., 40:2 (1999), 395–407 | Zbl

[4] Moldavanskii D.I., “Approksimiruemost konechnymi $p$-gruppami HNN-rasshirenii”, Vestn. Ivanovsk. gos. un-ta. Ser. “Biologiya, Khimiya, Fizika, Matematika”, 2000, no. 3, 129–140

[5] Tumanova E.A., “Ob approksimiruemosti kornevymi klassami grupp obobschennykh svobodnykh proizvedenii s normalnym ob'edineniem”, Izv. vuzov. Matem., 2015, no. 10, 27–44

[6] Tumanova E.A., “Ob approksimiruemosti kornevymi klassami HNN-rasshirenii grupp”, Model. i analiz inform. sistem, 21:4 (2014), 148–180

[7] Tumanova E.A., “Ob approksimiruemosti konechnymi $\pi$-gruppami obobschennykh svobodnykh proizvedenii grupp”, Matem. zametki, 95:4 (2014), 605–614 | DOI | Zbl

[8] Azarov D.N., “Approksimiruemost nekotorymi klassami konechnykh grupp obobschennogo svobodnogo proizvedeniya grupp s normalnoi ob'edinennoi podgruppoi”, Sib. matem. zhupn., 56:2 (2015), 249–264 | Zbl

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

[10] Shirvani M., “On residually finite HNN-extensions”, Arch. Math., 44:2 (1985), 110–115 | DOI | MR | Zbl

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

[12] Baumslag G., “On the residual nilpotence of certain one-relator groups”, Communs. Pure and Appl. Math., 21:5 (1968), 491–506 | DOI | MR | Zbl

[13] Sokolov E.V., Ob otdelimosti podgrupp v nekotorykh klassakh konechnykh grupp, Diss. $\dotsc$ kand. fiz.-matem. nauk, Ivanovsk. gos. un-t, Ivanovo, 2003

[14] Lindon R., Shupp P., Kombinatornaya teoriya grupp, Mir, M., 1980

[15] Magnus V., Karras A., Soliter D., Kombinatornaya teoriya grupp, Nauka, M., 1974