NON-PRIMITIVE WORDS OF THE FORM pq~m

摘要

Let p, q be two distinct primitive words. According to Lentin-Schutzenberger [9], the language p(+) q(+) contains at most one non-primitive word and if pq(m) is not primitive, then m = 2 vertical bar p vertical bar/vertical bar q vertical bar + 3. In this paper we give a sharper upper bound, namely, m = left perpendicular vertical bar p vertical bar - 2/vertical bar q vertical bar + 2 right perpendicular , where left perpendicular x right perpendicular stands for the floor of x.