arXiv subjects

Ettore Marmo

Publications and source records attributed to Ettore Marmo.

3 recordsLinked to original sources

arXiv2025

Presenting the Zassenhaus Lie algebra by the Magnus Lie algebra

It is shown that the Zassenhaus restricted $\mathbb F_p$-Lie algebra of a (pro-p) group G can be presented by the Magnus Lie algebra of G. For the class of (pro-p) groups for which the terms of the lower central series are torsion-free, the Zassenhaus restricted $\mathbb F_p$-Lie algebra can be explicitly computed from the Magnus Lie algebra. These results apply to orientable surface groups, right-angled Artin groups, pure braid groups, fundamental groups of supersolvable hyperplane arrangements and fundamental groups of strictly supersolvable toric arrangements.

math.GR↗

arXiv2025

Toric arrangements and Bloch-Kato pro-$p$ groups

We prove a purely combinatorial obstruction for the Bloch-Kato property within the class of fundamental groups of complement manifolds of toric arrangements (i.e., arrangements of hypersurfaces in the complex torus). As a stepping stone we obtain a combinatorial obstruction for the cohomology of a supersolvable arrangement to be generated in degree 1. Our result allows us to prove that - for all prime numbers $p$, the pro-$p$ completion of the pure braid group on $k$ strands has the Bloch-Kato property if and only if $k\leq 3$; - for all prime numbers $p$, the pro-$p$ completion of the pure mapping class group of the sphere $S^2$ with $k$ punctures has the Bloch-Kato property if and only if $k\leq 4$.

math.GR↗

arXiv2022

Sharpness of saturated fusion systems on a Sylow $p$-subgroup of ${\rm G}_2(p)$

We prove that the Díaz-Park's sharpness conjecture holds for saturated fusion systems defined on a Sylow $p$-subgroup of the group ${\rm G}_2(p)$, for $p\geq 5$.

math.GR↗