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Dan Haran

Publications and source records attributed to Dan Haran.

8 recordsLinked to original sources
arXiv2022

Relatively projective pro-$p$ groups

It is known that the Kurosh Subgroup Theorem does not hold for pro-$p$ groups of big cardinality. However, a subgroup $G$ of a free pro-$p$ product is projective relative to the Kurosh family of subgroups. In this paper we prove the converse of this fact.

math.GR↗
arXiv2021

$Θ$-Hilbertianity and strong $Θ$-Hilbertianity

$Θ$-Hilbertianity and its strengthening, strong $Θ$-Hilbertianity, are two generalizations of Hilbertianity inspired by Jarden's definition of $p$-Hilbertianity and strong $p$-Hilbertianity. Jarden has asked whether the two notions defined by him are actually the same. We address this question in its more general version of $Θ$-Hilbertianity and show that for PRC, and, in particular, for PAC fields, $p$-Hilbertianity and strong $p$-Hilbertianity coincide.

math.NT↗
arXiv2010

Frobenius subgroups of free profinite products

We solve an open problem of Herfort and Ribes: Profinite Frobenius groups of certain type do occur as closed subgroups of free profinite products of two profinite groups. This also solves a question of Pop about prosolvable subgroups of free profinite products.

math.GR↗
arXiv2010

Permanence criteria for semi-free profinite groups

We introduce the condition of a profinite group being semi-free, which is more general than being free and more restrictive than being quasi-free. In particular, every projective semi-free profinite group is free. We prove that the usual permanence properties of free groups carry over to semi-free groups. Using this, we conclude that if k is a separably closed field, then many field extensions of k((x,y)) have free absolute Galois groups.

math.GR↗