SEMISIMPLE GROUPS WITH THE REWRITING PROPERTY Q(5)

Let n be an integer greater than 1, and let G be a group. A subset (x( 1),x(2),...,x(n)) Of n elements of G is said to be rewritable if there are distinct permutations pi and sigma of {1,2,...,n} such that x(pi( 1))x(pi(2))...x(pi(n)) = x(sigma(1))x(sigma(2))...x(sigma(n)). The gro up G is said to have the rewriting property Q(n), or to be n-rewritabl e, if every subset of n elements of G is rewritable. The main result o f this paper shows that the only nontrivial semisimple groups with the property Q(5) are the alternating group A(5), the symmetric group S-5 , the projective special linear group PSL(2, 7) and the projective gen eral linear group PGL(2, 7).