### J Howie and A G Williams

#### Abstract

A generalized triangle group is a group that can be presented in the form % \( G = < x,y | x^p=y^q=w(x,y)^r=1 > \) % where \$p,q,r\geq 2\$ and \$w(x,y)\$ is an element of the free product \$< x,y | x^p=y^q=1 >\$ involving both \$x\$ and \$y\$. % Rosenberger has conjectured that every generalized triangle group \$G\$ satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple \$(p,q,r)\$ is one of \$(3,3,2),\ (3,4,2),\ (3,5,2),\$ or \$(2,m,2)\$ where \$m=3,4,5,6,10,12,15,20,30,60\$. In this paper we show that the Tits alternative holds in the cases \$(p,q,r)=(2,m,2)\$ where \$m=6,10,12,15,20,30,60\$.