This article is cited in 13 papers

Projective metabelian groups and Lie algebras

V. A. Artamonov


Abstract: Suppose that $A_n$ is the variety of all abelian groups of exponent dividing $n\geqslant0$, and $A_n=A$ is the variety of all abelian groups. In this paper it is proved that projective metabelian $A_nA$-groups of finite rank are free. Moreover, it is proved that projective metabelian $k[Y_1^{\pm1},\dots,Y_r^{\pm1},Z_1,\dots,Z_s]$-Lie algebras of finite rank, where $k$ is a principal ideal ring, are free.
Bibliography: 9 titles.

UDC: 519.4

MSC: Primary 20E10, 20E15; Secondary 20E05, 17B30

Received: 01.09.1976

 English version: Mathematics of the USSR-Izvestiya, 1978, 12:2, 213–223

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