Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose $F$ is a nonabelian free group and $F/N_1$ and $F/N_2$ are amenable groups. Does it follow that $F/(N_1 \cap N_2)$ is amenable?

share|improve this question

1 Answer 1

up vote 3 down vote accepted

$F/N_1\cap N_2$ embeds into the product $F/N_1 \times F/N_2$ under the natural map. Since the class of amenable groups is closed under products and passing to subgroups, we see that $F/N_1\cap N_2$ is indeed amenable.

share|improve this answer

Your Answer

 
discard

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.