Date: Thu, 9 Jan 1997 16:10:39 -0800 (PST) From: Arturo MagidinHello, I am looking at dominions (in the sense of Isbell) in varieties of nilpotent groups. This ends up being related to special amalgams (amalgams of two isomorphic groups amalgamated over the same subgroup). I am wondering if anyone knows of references studying the residual nilpotency of the Schreier product of two (isomorphic) groups. Specifically, if I start with a nilpotent group G, and a subgroup H, and I look at the coproduct of two copies of G amalgamated over H, under what conditions is this residually nilpotent? I am particularly interested in the case when H is not normal. I have a paper with the sufficient and necessary conditions for the free product of nilpotent groups to be residually nilpotent (this would be the case of H trivial), but presumably for more general amalgams the conditions are much different. Thank you for any help or references. Regards, Arturo Magidin magidin@math.berkeley.edu