Calculating the set of orders of elements in the finite linear groups. (English) Zbl 1154.20040

Summary: Let \(q\) be a power of the prime \(p\). The general and special linear groups in dimension \(n\) over the Galois field \(F_q\) are denoted by \(\text{GL}_n(q)\) and \(\text{SL}_n(q)\), respectively, and the projective versions of these groups are indicated by \(\text{PGL}_n(q)\) and \(\text{PSL}_n(q)\). 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 are given in the text.


20G40 Linear algebraic groups over finite fields
20D60 Arithmetic and combinatorial problems involving abstract finite groups
68W30 Symbolic computation and algebraic computation
20-04 Software, source code, etc. for problems pertaining to group theory
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