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)