Let $G$ be a free product of 2 groups with $G \neq Z_2*Z_2$ . i would like to know if the following assertion is correct :
Every almost nilpotent subgroup of G is contained in a unique maximal almost nilpotent subgroup .
Let $G$ be a free product of 2 groups with $G \neq Z_2*Z_2$ . i would like to know if the following assertion is correct :
Every almost nilpotent subgroup of G is contained in a unique maximal almost nilpotent subgroup .
Read 1.1 here http://tinyurl.com/d3ybkmg
As the modular group $\,C_2*C_3\,$ is not torsion free, we cannot be sure of the existence of max. virt. nilpotent subgroups, as remarked in the above paper, yet I still don't fully understand Steve's point as why would we care about what happens to a subgroup containing two subgroups?