More of a question than a problem really, but so what? GCS ------------------------------------------------------------ Date: Tue, 03 Dec 1996 15:53:35 -0600 From: isaacs@math.wisc.edu Subject: repeated commutators Let A act on G where A and G are finite and let [G,A,A, ... ,A] = K. Finally, let B be the largest subgroup of A such that [G,B] is contained in K. (Thus B is the kernel of the action of A on the set of right cosets of K in G.) I found some old notes in my handwriting that prove (among other things) that if K contains some term of the derived series of G then A/B is solvable. I do not know from where I got this result. It is even possible that I discovered it. My question is: does anyone have a reference for this; is it actually a known result? Remark: If K is normal in G, it is no loss to assume that K = 1 and in that case, A/B is actually nilpotent by a result of P. Hall. (Without any solvability assumption on G.) My interest, therefore, is specifically in the case where K is not normal, and is, in fact core-free. I. M. Isaacs isaacs@math.wisc.edu