NON-ABELIAN TENSOR ABSOLUTE CENTRE OF A GROUP

In 1904, Schur proved his famous result which says that if the central factor group of a given group is finite then so is its derived subgroup. In 1994, Hegarty showed that if the absolute central factor group, G L(G), is finite then so is its autocommutator subgroup, K(G).Using the notion of non-abelian tensor product, we introduce the concept of tensor absolute centre, L^otimes (G)$, and K^otimes(G)=Gotimes { m Aut}(G). Then under some condition we prove that the finiteness of GL^otimes(G) implies that K^otimes(G) is also finite.