Abstract Let ₖ=x₁, , xₖ γ k = x 1, ⋯, x k be the k -th lower central group-word. Given a group G, we write Xₖ (G) X k (G) for the set of ₖ γ k -values and ₖ (G) γ k (G) for the k -th term of the lower central of G. This paper deals with groups in which g^Xₖ (G) ⟨ g X k (G) ⟩ is a Chernikov group of size at most (m, n) for all g G g ∈ G. The main result is that ₊+₁ (G) γ k + 1 (G) is a Chernikov group and its size is (k, m, n) -bounded.
Capasso et al. (Thu,) studied this question.
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