Calculating the set of orders of elements in the finite linear groups

Abstract

Let q be a power of the prime p. The general and special linear groups in dimension n over the Galois field F _q is denoted by GL _n (q) and SL _n (q) respectively and the projective versions of these groups are indicated by PGL _n (q) and PSL _n (q). Using polynomials of degree n over F _q we show how it is possible to find the set of orders of elements in the above groups. This is achieved by writing computer programs whose details will be given in the text.

Keywords:

• General linear group
• special linear group
• elements order
• finite field
• algorithm