Geodesic
Free decompositions in varieties of $\Lambda$-groups
Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 389-407 
S. V. Polin. Free decompositions in varieties of $\Lambda$-groups. Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 389-407. http://geodesic.mathdoc.fr/item/SM_1972_16_3_a5/
@article{SM_1972_16_3_a5,
     author = {S. V. Polin},
     title = {Free decompositions in varieties of $\Lambda$-groups},
     journal = {Sbornik. Mathematics},
     pages = {389--407},
     year = {1972},
     volume = {16},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_16_3_a5/}
}
TY  - JOUR
AU  - S. V. Polin
TI  - Free decompositions in varieties of $\Lambda$-groups
JO  - Sbornik. Mathematics
PY  - 1972
SP  - 389
EP  - 407
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1972_16_3_a5/
LA  - en
ID  - SM_1972_16_3_a5
ER  - 
%0 Journal Article
%A S. V. Polin
%T Free decompositions in varieties of $\Lambda$-groups
%J Sbornik. Mathematics
%D 1972
%P 389-407
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1972_16_3_a5/
%G en
%F SM_1972_16_3_a5

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

This paper is concerned with $\Lambda$-groups, i.e. groups with powers from a field $\Lambda$ of characteristic $0$. Particular examples of $\Lambda$-groups are complete groups with single valued root extraction ($D$-groups). It is proven that in the variety of $\Lambda$-groups theorems concerning the decomposition of $\Lambda$-subgroups of a free product of $\Lambda$-groups and free $\Lambda$-subgroups of a free $\Lambda$-group are valid. Bibliography: 6 titles.

[1] G. Baumslag, “Some aspects of groups with unique roots”, Acta Math., 104:1 (1960), 217–303 | DOI | MR | Zbl

[2] A. G. Kurosh, Teoriya grupp, Nauka, Moskva, 1967 | MR | Zbl

[3] H. W. Kuhn, “Subgroup theorem for groups presented by generators and relations”, Ann. Math., 56:1 (1952), 22–46 | DOI | MR | Zbl

[4] B. I. Plotkin, Gruppy avtomorfizmov algebraicheskikh sistem, Nauka, Moskva, 1966 | MR | Zbl

[5] S. MacLane, “A proof of the subgroup theorem for free products”, Mathematika, 5:9 (1958), 13–19 | MR | Zbl

[6] A. G. Kurosh, Lektsii po obschei algebre, Fizmatgiz, Moskva, 1962 | MR