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On residually finite groups and their generalizations. (English) Zbl 0941.20033
A group $$G$$ is called a finite embedding group (FE-group) if for every finite subset $$X$$ of $$G$$ there exists an injection $$\Psi$$ of $$X$$ into a finite group $$H$$ such that if $$x,y$$ and $$xy$$ are in $$X$$ then $$\Psi(xy)=\Psi(x)\Psi(y)$$. In this paper a family of three generator soluble FE-groups with torsion-free Abelian factors which are not residually finite is constructed.

##### MSC:
 20E26 Residual properties and generalizations; residually finite groups 20F16 Solvable groups, supersolvable groups
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