# On elements in algebras having finite number of conjugates

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## Abstract

Let R be a ring with unity and U(R) its group of units. Let Delta U = {a is an element of U(R) \textbackslash [U(R) : C-U(R)(a)] < infinity} be the FC-radical of U(R) and let del(R) = {a is an element of R \textbackslash [U(R) : C-U(R)(a)] < infinity} be the FC-subring of R. An infinite subgroup H of U(R) is said to be an omega-subgroup if the left annihilator of each nonzero Lie commmutator [x, y] in R contains only finite number of elements of the form 1 - h, where x, y is an element of R and h is an element of H. In the case when R is an algebra over a field F, and U(R) contains an omega-subgroup, we describe its FC-subalgebra and the FC-radical. This paper is an extension of [1].

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