Author

Matteo Vannacci

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Preprint Sep 2026

Virtually generating graphs of pro-$p$ groups

We study the virtually generating graph of pro-$p$ groups. We show that various classes of pro-$p$ groups have connected virtually generating graph and we bound its diameter in these cases; e.g.\ compact subgroups of analytic groups over local fields and the Nottingham group.

Y. Barnea, Andrea Lucchini, Margherita Piccolo et al. · 0 citations

Preprint Jul 2026

Engel probability in wreath products of $p$-groups

We give upper and lower bounds for the number of solutions of the equation $e_n(x,y) = g$ in the group $W_k=(C_p\wr C_{p^k})^2$, where $e_n(x,y)$ is the $n$-th Engel word and $g\in W_k$. We obtain several corollaries from this. First, we prove a stronger version of the Amit-Ashurst conjecture for Engel words in $W_k$....

Iker Heras, Tommaso Toti, Matteo Vannacci · 0 citations