Abstract
We study a group G containing an element g such that CG(g)∩gG is finite. The nonoriented graph Γ is defined as follows. The vertex set of Γ is the conjugacy class gG. Vertices x and y of the graph G are bridged by an edge iff x≠y and xy=yx. Let Γ0 be some connected component of G. On a condition that any two vertices of Γ0 generate a nilpotent group, it is proved that a subgroup generated by the vertex set of Γ0 is locally nilpotent.
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Additional information
Supported by the RF State Committee of Higher Education.
Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 637–650, November–December, 1998.
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Kislyakov, V.E. Groups containing an element that permutes with a finite number of its conjugates. Algebr Logic 37, 363–370 (1998). https://doi.org/10.1007/BF02671690
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DOI: https://doi.org/10.1007/BF02671690