The kernel generating condition and absolute Galois groups

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For a list ℒ of finite groups and for a profinite group G, we consider the intersection T(G) of all open normal subgroups N of G with G/N in ℒ . We give a cohomological characterization of the epimorphisms π:S → G of profinite groups (satisfying some additional requirements) such that π[T(S)] = T(G). For p prime, this is used to describe cohomologically the profinite groups G whose nth term G (n,p) (resp., G (n,p)) in the p-Zassenhaus filtration (resp., lower p-central filtration) is an intersection of this form. When G = GF is the absolute Galois group of a field F containing a root of unity of order p, we recover as special cases results by Mináč, Spira and the author, describing G (3,p) and G(3,p) as T(G) for appropriate lists ℒ .

Original languageAmerican English
Pages (from-to)217-250
Number of pages34
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Nov 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics


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