Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 .

share|cite|improve this question
How could it be true? Take $G=C_2\ast C_3$, and consider the two subgroups $C_2$ and $C_3$. The only subgroup that contains both of them is all of $G$, which is certainly not virtually nilpotent (being virtually free and all). – user641 May 17 '12 at 17:59

Read 1.1 here

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?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.