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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:
 2e+16 Chains and lattices of subgroups, subnormal subgroups
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