Giorgio Leoni | Searcharxiv

arXiv2026

Cohomology rings and $p$-local behavior of even Artin groups

We generalize to certain families of even Artin groups several classical results on right-angled Artin groups. In particular, we compute the cohomology ring, describe the pro-$p$ completion, and determine the $p$-Zassenhaus restricted Lie algebra in the FC case. As a by-product, we prove a rigidity result that implies that if two even Artin groups of FC type are isomorphic, then for every prime $p$, the $p$-parts of their defining graphs are isomorphic.

math.GR↗

arXiv2026

Generalising a Theorem of Lichtman

We show that under a suitable additional hypothesis the restricted Zassenhaus $\F_p$-Lie algebra or the rational Magnus Lie algebra of a free amalgamated product is the free amalgamated product of the corresponding Lie algebras of the factors. This generalises a Theorem of A.I.\,Lichtman, who proved the analoguous statement for free products. Our conditions include the case when the amalgamated product is a retract in both factors. As a by-product, we show that a free product of residually torsion free nilpotent groups amalgamated along retracts is also residually torsion free nilpotent and obtain also some results on cohomological completeness. In the final sections we apply our main results to two recently raised open questions.

math.GR↗