On the descending central sequence of absolute Galois groups
I Efrat, J Mináč - American journal of mathematics, 2011 - muse.jhu.edu
I Efrat, J Mináč
American journal of mathematics, 2011•muse.jhu.eduLet $ p $ be an odd prime number and $ F $ a field containing a primitive $ p $ th root of
unity. We prove a new restriction on the group-theoretic structure of the absolute Galois
group $ G_F $ of $ F $. Namely, the third subgroup $ G_F^{(3)} $ in the descending $ p $-
central sequence of $ G_F $ is the intersection of all open normal subgroups $ N $ such that
$ G_F/N $ is $1 $, ${\Bbb Z}/p^ 2$, or the extra-special group $ M_ {p^ 3} $ of order $ p^ 3$
and exponent $ p^ 2$.
unity. We prove a new restriction on the group-theoretic structure of the absolute Galois
group $ G_F $ of $ F $. Namely, the third subgroup $ G_F^{(3)} $ in the descending $ p $-
central sequence of $ G_F $ is the intersection of all open normal subgroups $ N $ such that
$ G_F/N $ is $1 $, ${\Bbb Z}/p^ 2$, or the extra-special group $ M_ {p^ 3} $ of order $ p^ 3$
and exponent $ p^ 2$.
Let be an odd prime number and a field containing a primitive th root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group of . Namely, the third subgroup in the descending -central sequence of is the intersection of all open normal subgroups such that is , , or the extra-special group of order and exponent .
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