On groups generated by elements of prime order (Q1301610)

Let \(F\) be a field containing a primitive \(p\)th root of unity, where \(p\) is a prime number. The authors show that every element in \(SL_n(F)\) is a product of \(4\) or fewer elements of order \(p.\) They investigate which subgroups of the general linear group are generated by elements of order \(p,\) and they search for the existence of some integer \(k\) such that every element in the group can be expressed by \(k\) or fewer elements of order \(p.\) The authors pursue similar questions also for abstract groups.