The problem of integral similarity of block-triangular matrices over the ring of integers is connected to that of finding representatives of the classes of an equivalence relation on general integer matrices. A complete list of representatives of conjugacy classes of torsion in the 4 × 4 general linear group over ring of integers is given. There are 45 distinct such classes and each torsion element has order of 1, 2, 3, 4, 5, 6, 8, 10 or 12.

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ABSTRACT. In this note we determine which dihedral subgroups of GL g (C) can be realized by group actions on Riemann surfaces of genus g Ù 1.

A complete list of realizable conjugacy classes of torsion in the 4 × 4 integral symplectic group by analytic automorphisms of compact connected Riemann surfaces of genus two is given.