17.110 (2010)
Opena) Is it true that for each word $w$, there is a function $h: \mathbb{N} \times \mathbb{N} \to \mathbb{N}$ such that the width of $w$ in every finite $p$-group of Prüfer rank $r$ is bounded by $h(p, r)$?
b) If so, can $h(p, r)$ be made independent of $p$?
Progress
An affirmative answer to a) would imply A. Jaikin-Zapirain's result (ibid.) that every word has finite width in each $p$-adic analytic pro-$p$ group, since a pro-$p$ group is $p$-adic analytic if and only if the Prüfer ranks of all its finite quotients are uniformly bounded.
Proof claims
Proof claims are the responsibility of the submitter. Appearance here does not mean the claim has been checked for mathematical correctness.
Moderators only screen for spam, abuse, and obviously low-effort submissions.
No proof claims yet.
Log in to claim a proof.
Comments
No comments yet. Be the first to comment.
Log in to post a comment.