The main purpose of this article is to study pro-p groups with quadratic -cohomology algebra, i.e.-quadratic pro-p groups. Prime examples of such groups are the maximal Galois pro-p groups of fields containing a primitive root of unity of order p. We show that the amalgamated free product and HNN-extension of-quadratic pro-p groups is -quadratic, under certain necessary conditions. Moreover, we introduce and investigate a new family of pro-p groups that yields many new examples of -quadratic groups: p-RAAGs. These examples generalise right angled Artin groups in the category of pro-p groups. Finally, we explore “Tits alternative behaviour” of -quadratic pro-p groups.

On pro-p groups with quadratic cohomology

Quadrelli, C.
;
2022-01-01

Abstract

The main purpose of this article is to study pro-p groups with quadratic -cohomology algebra, i.e.-quadratic pro-p groups. Prime examples of such groups are the maximal Galois pro-p groups of fields containing a primitive root of unity of order p. We show that the amalgamated free product and HNN-extension of-quadratic pro-p groups is -quadratic, under certain necessary conditions. Moreover, we introduce and investigate a new family of pro-p groups that yields many new examples of -quadratic groups: p-RAAGs. These examples generalise right angled Artin groups in the category of pro-p groups. Finally, we explore “Tits alternative behaviour” of -quadratic pro-p groups.
2022
2022
https://www.sciencedirect.com/science/article/abs/pii/S0021869322004197
Quadratic cohomology, maximal pro-p Galois groups, Demushkin groups, free pro-p constructions, Right angled Artin groups, uniform pro-p groups
Quadrelli, C.; Snopce, I.; Vannacci, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2139751
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