Free decompositions in varieties of $\Lambda$-groups
Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 389-407 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
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     title = {Free decompositions in varieties of $\Lambda$-groups},
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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/

[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