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

Darafsheh, M. R.; Farjami, Y.

J. Discrete Math. Sci. Cryptography 10, No. 5, 637-653 (2007).

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.

MSC:

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

Keywords:

general linear groups; special linear groups; element orders; finite fields; algorithms

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