Date: Wed, 11 Sep 96 16:06:09 -0400 Sender: alperin@riemann From: "Roger Alperin - Sponsored by K.Brown"To: group-pub-forum@maths.bath.ac.uk For a while I've been playing with the family of presenations for n odd and (a,c)=1 Other than n=3, a=2, c=1 (or slight variations) the groups turn out to be infinite. Rarely can I find a subgroup of finite index mapping onto Z. Lately I've been trying quotpic and descending down some p-series and applying Newman's version of the Golod-Shafarevich theorem to get that the group is infinite. I do know that there is a finite quotient of order n|a^n+c^n|. I've begun to suspect that these groups are non-Hopfian. Anyone have some suggestions? I did try to apply small cancellation a long time agao but didn't see how to get it to work, but I'm open to trying that too with some hints as to how to change the presentation. Thanks, Roger Alperin (see Proc. Royal Soc. Edinburgh, 1991, 118A, pp 289-294)