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Progress in Galois Theory - Proceedings of John Thompson's 70th Birthday Conference (Paperback, Softcover reprint of hardcover 1st ed. 2005)
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Progress in Galois Theory - Proceedings of John Thompson's 70th Birthday Conference (Paperback, Softcover reprint of hardcover 1st ed. 2005)
Series: Developments in Mathematics, 12
Expected to ship within 10 - 15 working days
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The legacy of Galois was the beginning of Galois theory as well as
group theory. From this common origin, the development of group
theory took its own course, which led to great advances in the
latter half of the 20th cen tury. It was John Thompson who shaped
finite group theory like no-one else, leading the way towards a
major milestone of 20th century mathematics, the classification of
finite simple groups. After the classification was announced around
1980, it was again J. Thomp son who led the way in exploring its
implications for Galois theory. The first question is whether all
simple groups occur as Galois groups over the rationals (and
related fields), and secondly, how can this be used to show that
all finite groups occur (the 'Inverse Problem of Galois Theory').
What are the implica tions for the stmcture and representations of
the absolute Galois group of the rationals (and other fields)?
Various other applications to algebra and number theory have been
found, most prominently, to the theory of algebraic curves (e.g.,
the Guralnick-Thompson Conjecture on the Galois theory of covers of
the Riemann sphere)."
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