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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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