Date: Thu, 9 Jan 1997 16:10:39 -0800 (PST)
From: Arturo Magidin 

Hello,
 
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