This article is cited in 1 paper

On verbal factors of almost free groups in varieties

S. V. Rychkov

Orekhovo-Zuevo Pedagogical Institute

Abstract: Under the assumption of the axiom of constructibility of set theory it is shown that for varieties of groups of exponent zero and for uncountable, regular, not weakly compact cardinals $k$ there can be constructed $k$-separable groups having no nontrivial decomposition into a verbal product.

UDC: 512

MSC: Primary 20E05, 20E10; Secondary 20A15

Received: 13.03.1990

 English version: Mathematics of the USSR-Sbornik, 1992, 73:2, 501–516

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