CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.50, no.1, pp.67-74, 2000 (Journal Indexed in SCI)
G(3, m, n) is the group presented by [a, b \ a(5) = (ab)(2) = b(m+3)a(-n)b(m)a(-n) = 1]. In this paper, we study the structure of G(3, m, n). We also give a new efficient presentation for the Projective Special Linear group PSL(2, 5) and in particular we prove that PSL(2, 5) is isomorphic to G(3, m, n) under certain conditions.