Finitely valued commutator sequences

Abstract

If x and y are elements in the group G, then we denote their commutator by x o y = x-1y-1 = x-1xy; and x o G is the set of all commutators x o g with g ∈ G. A G-commutator sequence is a series of elements ci ∈ G with c1 + 1 ∈ ci O G. Slightly generalizing well known results one proves that the hypercenter of the group G is exacly the set of all elements h ∈ G with the property: every G-commutator sequence, containing h, contains 1 [Proposition 1.1].