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
