Geodesic
Subgroups satisfying an identity in a class of abstract groups
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 371-386 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A description is obtained of the subgroups of groups acting on a tree that do not contain nonabelian free subgroups; it is a new interpretation of a result of Bass. The author considers the class $\mathscr G$ consisting of all groups constructive from cyclic groups using amalgamated free products and HNN-extensions, with certain restrictions. A description is obtained of all the subgroups of groups in $\mathscr G$ that satisfy identities, and it is shown that the groups in $\mathscr G$ satisfy the Tits alternative. The proof uses the techniques of group actions on trees. 
@article{SM_1992_71_2_a6,
     author = {Yu. V. Tishin},
     title = {Subgroups satisfying an identity in a~class of abstract groups},
     journal = {Sbornik. Mathematics},
     pages = {371--386},
     year = {1992},
     volume = {71},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a6/}
}
TY  - JOUR
AU  - Yu. V. Tishin
TI  - Subgroups satisfying an identity in a class of abstract groups
JO  - Sbornik. Mathematics
PY  - 1992
SP  - 371
EP  - 386
VL  - 71
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1992_71_2_a6/
LA  - en
ID  - SM_1992_71_2_a6
ER  - 
%0 Journal Article
%A Yu. V. Tishin
%T Subgroups satisfying an identity in a class of abstract groups
%J Sbornik. Mathematics
%D 1992
%P 371-386
%V 71
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1992_71_2_a6/
%G en
%F SM_1992_71_2_a6
Yu. V. Tishin. Subgroups satisfying an identity in a class of abstract groups. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 371-386. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a6/

[1] Serr Zh.-P., “Derevya, amalgamy i $SL_2$”, Matematika, 18 (1974), 3–51 | Zbl

[2] Serre J.-P., Trees, Springer Verlag, Berlin - Heidelberg - New York, 1980 | MR | Zbl

[3] Lindon R., Shupp P., Kombinatornaya teoriya grupp, Mir, M., 1980 | MR

[4] Bass H., “Some remarks on group actions on trees”, Communs. in Algebra, 4 (1976), 1091–1126 | DOI | MR | Zbl

[5] Karras A., Solitar D., “Subgroups of $HNN$ groups and groups with one defining relation”, Can. J. Math., 23 (1971), 627–643 | MR | Zbl

[6] Cossey J., Smythe B., “$HNN$ groups and groups with center”, Ann. Math. Stud., 1975, no. 84, 87–89 | MR

[7] Chebotar A. A., “Podgruppy s odnim opredelyayuschim sootnosheniem, ne soderzhaschie svobodnykh podgrupp ranga 2”, Algebra i logika, 10 (1971), 570–586 | Zbl

[8] Chebotar A. A., “Podgruppy grupp s odnim opredelyayuschim sootnosheniem, obladayuschie normalnymi delitelyami, udovletvoryayuschimi tozhdestvu”, Sib. matem. zhurn., 16 (1975), 139–148 | Zbl

[9] Durnev V. G., O podgruppakh $F$-grupp, Dep. v VINITI, 1987. No4039-V87

[10] Tishin Yu. V., “Normalnye podgruppy svobodnykh konstruktsii”, Matem. sb., 126(168) (1985), 377–396 | MR | Zbl

[11] Tishin Yu. V., “Stroenie podgrupp, udovletvoryayuschikh netrivialnomu tozhdestvu, v nekotorom klasse abstraktnykh grupp”, DAN BSSR, 33:5 (1989), 393–395 | MR | Zbl