8.44 (1982)

Prove or disprove that for all but finitely many primes $p$, the group
$$G_p = \langle a, b \mid a^2 = b^p = (ab)^3 = (b^r ab^{-2r} a)^2 = 1 \rangle,$$ where $r^2 + 1 \equiv 0 \pmod{p}$, is infinite. A solution of this problem would have interesting topological applications.