Dear all,
I came across the above group (for any fixed odd prime $p$) and would need to know if it's large or not. It seems like it shouldn't be...
Best wishes, Elisabeth
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.
Sign up to join this communityDear all,
I came across the above group (for any fixed odd prime $p$) and would need to know if it's large or not. It seems like it shouldn't be...
Best wishes, Elisabeth
The group $G$ maps onto the free product $C_p*C_p*C_p$ of three cyclic groups of order $p$ (just send each $b_i^p$ to $1$). This free product is virtually free, as a free product of finite groups (by Kurosh theorem the kernel of the homomorphism onto $C_p \times C_p \times C_p$ is free) and is not virtually cyclic. Hence it is large, and so $G$ is large as well. This works for any $p>1$.