О порождающих множествах матричных групп над конечными полями

It is proved that the group of all (n × n)-matrices with determinant ±1 over a finite field of q elements for odd q is generated by three involutions, two of which commute, if and only if n > 5. It is also established that for n > 5 this group is the automorphism group of a regular 3-polytope of type [4p, n] or [4p, 2n], where q is a power of a prime number p