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Groups as Galois Groups
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  • Cited by 34
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Coccia, Simone 2019. The Hilbert Property for integral points of affine smooth cubic surfaces. Journal of Number Theory,

    Bary-Soroker, Lior and Schlank, Tomer M. 2018. SIEVES AND THE MINIMAL RAMIFICATION PROBLEM. Journal of the Institute of Mathematics of Jussieu, p. 1.

    König, Joachim 2018. On intersective polynomials with non-solvable Galois group. Communications in Algebra, Vol. 46, Issue. 6, p. 2405.

    Chen, William Yun 2018. Moduli interpretations for noncongruence modular curves. Mathematische Annalen, Vol. 371, Issue. 1-2, p. 41.

    Corvaja, Pietro and Zannier, Umberto 2017. On the Hilbert property and the fundamental group of algebraic varieties. Mathematische Zeitschrift, Vol. 286, Issue. 1-2, p. 579.

    Bridy, Andrew and Garton, Derek 2017. Dynamically distinguishing polynomials. Research in the Mathematical Sciences, Vol. 4, Issue. 1,

    Paulhus, Jennifer and Rojas, Anita M. 2017. Completely Decomposable Jacobian Varieties in New Genera. Experimental Mathematics, Vol. 26, Issue. 4, p. 430.

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

    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.

    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.

    Barkatou, Moulay A. Cluzeau, Thomas and Jalouli, Achref 2015. Formal Solutions of Linear Differential Systems with Essential Singularities in their Coefficients. p. 45.

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

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

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

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

    Knyazhansky, Marina and Plotkin, Tatjana 2012. Knowledge Bases Over Algebraic Models. International Journal of Knowledge Management, Vol. 8, Issue. 1, p. 22.

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

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


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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