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Groups as Galois Groups
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  • Cited by 25
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bachmayr, Annette Harbater, David and Hartmann, Julia 2016. Differential Galois groups over Laurent series fields. Proceedings of the London Mathematical Society, Vol. 112, Issue. 3, p. 455.

    Burda, Y. and Khovanskii, A. 2016. Polynomials Invertible in k-Radicals. Arnold Mathematical Journal, Vol. 2, Issue. 1, p. 121.

    Cherednik, Ivan 2016. On Galois action in rigid DAHA modules. International Mathematics Research Notices, p. rnw034.

    Barkatou, Moulay A. Cluzeau, Thomas and Jalouli, Achref 2015. Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15. p. 45.

    Grizzard, Robert Habegger, Philipp and Pottmeyer, Lukas 2015. Small Points and Free Abelian Groups. International Mathematics Research Notices, Vol. 2015, Issue. 20, p. 10657.

    Schwarz, João Fernando 2015. Some aspects of noncommutative invariant theory and the Noether’s problem. São Paulo Journal of Mathematical Sciences, Vol. 9, Issue. 1, p. 62.

    Garion, Shelly and Penegini, Matteo 2014. Beauville Surfaces, Moduli Spaces and Finite Groups. Communications in Algebra, Vol. 42, Issue. 5, p. 2126.

    Bary-Soroker, Lior and Paran, Elad 2013. Fully Hilbertian fields. Israel Journal of Mathematics, Vol. 194, Issue. 2, p. 507.

    Harbater, David Hartmann, Julia and Krashen, Daniel 2013. Weierstrass preparation and algebraic invariants. Mathematische Annalen, Vol. 356, Issue. 4, p. 1405.

    Baba, Shinpei 2012. Complex Projective Structures with Schottky Holonomy. Geometric and Functional Analysis, Vol. 22, Issue. 2, p. 267.

    Plotkin, Tatjana and Knyazhansky, Marina 2012. Symmetries of knowledge bases. Annals of Mathematics and Artificial Intelligence, Vol. 64, Issue. 4, p. 369.

    Amram, Meirav Dettweiler, Michael and Teicher, Mina 2010. On rigid covers associated to the three-cuspidal quartic. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 80, Issue. 1, p. 1.

    Brink, David 2010. Hölder Continuity of Roots of Complex andp-adic Polynomials. Communications in Algebra, Vol. 38, Issue. 5, p. 1658.

    Fried, Michael D. 2010. Alternating groups and moduli space lifting invariants. Israel Journal of Mathematics, Vol. 179, Issue. 1, p. 57.

    Harbater, David and Hartmann, Julia 2010. Patching over fields. Israel Journal of Mathematics, Vol. 176, Issue. 1, p. 61.

    Cadoret, Anna and Dèbes, Pierre 2009. Abelian constraints in inverse Galois theory. manuscripta mathematica, Vol. 128, Issue. 3, p. 329.

    Cadoret, Anna 2005. Counting real Galois covers of the projective line. Pacific Journal of Mathematics, Vol. 219, Issue. 1, p. 53.

    Cook, William J. Mitschi, Claude and Singer, Michael F. 2005. On the Constructive Inverse Problem in Differential Galois Theory#. Communications in Algebra, Vol. 33, Issue. 10, p. 3639.

    Hallouin, Emmanuel and Riboulet-Deyris, Emmanuel 2003. Computation of some moduli spaces of covers and explicit 𝒮nand 𝒜nregular ℚ(T)-extensions with totally real fibers. Pacific Journal of Mathematics, Vol. 211, Issue. 1, p. 81.

    Hwang, Y.-S. Leep, David B. and Wadsworth, Adrian R. 2003. Galois groups of order 2n that contain a cyclic subgroup of order n. Pacific Journal of Mathematics, Vol. 212, Issue. 2, p. 297.

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    Groups as Galois Groups
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Book description

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realisation of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.


Review of the hardback:‘I highly recommend this book to all readers who like to learn this aspect of Galois theory, those who like to give a course on Galois theory and those who like to see how different mathematical methods as analysis, Riemann surface theory and group theory yield a nice algebraic result.’

Translated from Martin Epkenhans Source: Zentralblatt für Mathematiche

Review of the hardback:‘… a very helpful introduction into an active research area, recommended for graduate students and anyone interested in recent progress in the inverse Galois problem.’

B. H. Matzat Source: Bulletin of London Mathmatical Society

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