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Imbedding of some wreath products in automorphism groups of finitely-generated solvable groups. (Russian) Zbl 0358.20042
Let \(G\) be a finitely generated solvable group, \(A \subseteq \mathrm{Aut}\;G\) a subgroup of automorphisms acting trivial on \(G/G'\). Theorem. A wreath product of \(A\) and an infinite cyclic group is embeddable in \(\mathrm{Aut}\;H\) for some finitely generated solvable group \(H\). Corollary. Let \(A\) be a finitely generated group which is a finite extension of a solvable group. Then \(A\) wr \(Z\) is embeddable in \(\mathrm{Aut}\;H\) for some finitely generated solvable group \(H\), \(Z\) being the group of integers. This presents a negative solution of a question of S. Bachmuth and H. Y. Mochizuki [Bull. Am. Math. Soc. 81, 420–422 (1975; Zbl 0299.20025)].

MSC:
20E15 Chains and lattices of subgroups, subnormal subgroups
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