Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion

Author:

Bar-On Tamar1

Affiliation:

1. Department of Mathematics , 98592 University of Oxford Mathematical Physical and Life Sciences Division , Oxford , OX2 6GG , United Kingdom

Abstract

Abstract Let p be a prime number. One of the most difficult and important questions in Galois theory these days is determining which pro-p groups can occur as maximal pro-p Galois groups. Some restrictions of the structure of maximal pro-p Galois groups are already known, and therefore, the families of all pro-p groups satisfying these restrictions are in the center of the research. In the current paper we deal with three of these families: The family of all pro-p groups which satisfy hereditarily the n-vanishing Massey product property, the family of 1-cyclotomic oriented pro-p groups, and the family of pro-p groups that are hereditarily of p-absolute Galois type. We show that all these families are closed under taking profinite completion of each order.

Publisher

Walter de Gruyter GmbH

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