This article is cited in 1 paper

Free decompositions in varieties of $\Lambda$-groups

S. V. Polin


Abstract: 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.

UDC: 519.41/47

MSC: Primary 20E30; Secondary 20F05

Received: 16.03.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 16:3, 389–407

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