Results 21 to 30 of about 70 (70)

Actions of the absolute Galois group [PDF]

, 2016
We review some ideas of Grothendieck and others on actions of the absolute Galois group Q of Q (the automorphism group of the tower of finite extensions of Q), related to the geometry and topology of surfaces (mapping class groups, Teichm{ }ller spaces and moduli spaces of Riemann surfaces). Grothendieck's motivation came in part from his desire to
A'Campo, Norbert, Ji, Lizhen, Papadopoulos, Athanase   +2 more
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On realizability of $p$-groups as Galois groups

, 2011
In this article we survey and examine the realizability of $p$-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension ...
Michailov, Ivo M., Ziapkov, Nikola P.
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Block Systems of a Galois Group [PDF]

Experimental Mathematics, 1995
We describe an algorithm to compute subfields of an algebraic number field as block systems of its Galois group. It relies only on symbolic computations and avoids numerical approximations.
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A GALOIS EXTENSION WITH GALOIS GROUP DIHEDRAL GROUP OR GENERALIZED QUATERNION GROUP

Communications of the Korean Mathematical Society, 2005
Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L() where . We show that if , and [N : L] = m, then or generalized quaternion group whether , respectively.
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Cohomology of absolute Galois groups

, 2014
The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-$p$ case, i.e., one would like to know which pro-$p$ groups occur as maximal pro-$p$ Galois groups, i.e ...
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Galois Groups and Complex Multiplication [PDF]

Transactions of the American Mathematical Society, 1978
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On the structure of Galois groups as Galois modules [PDF]

, 1984
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Galois cohomology of abelian groups [PDF]

Pacific Journal of Mathematics, 1968
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Galois Groups, Galois Representations and Iwasawa Theory

Journal of the Indian Institute of Science, 2022
In this article, the author provides a lively picture of the principal questions and the main results in Iwasawa theory. After briefly explaining the role of Leopoldt's conjecture in connection with the number of independent \(\mathbb Z_p\)-extensions of number fields, she introduces Galois representations and mentions the Tate module of elliptic ...
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On 2-Groups as Galois Groups

Canadian Journal of Mathematics, 1995
AbstractLetL/Kbe a finite Galois extension in characteristic ≠ 2, and consider a non-split Galois theoretical embedding problem overL/Kwith cyclic kernel of order 2. In this paper, we prove that if the Galois group ofL/Kis the direct product of two subgroups, the obstruction to solving the embedding problem can be expressed as the product of the ...
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