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A consistent and near complete survey of the important progress
made in the field over the last few years, with the main emphasis
on the rigidity method and its applications. Among others, this
monograph presents the most successful existence theorems known and
construction methods for Galois extensions as well as solutions for
embedding problems combined with a collection of the existing
Galois realizations.
A consistent and near complete survey of the important progress
made in the field over the last few years, with the main emphasis
on the rigidity method and its applications. Among others, this
monograph presents the most successful existence theorems known and
construction methods for Galois extensions as well as solutions for
embedding problems combined with a collection of the existing
Galois realizations.
This book presents state-of-the-art research and survey articles
that highlight work done within the Priority Program SPP 1489
"Algorithmic and Experimental Methods in Algebra, Geometry and
Number Theory", which was established and generously supported by
the German Research Foundation (DFG) from 2010 to 2016. The goal of
the program was to substantially advance algorithmic and
experimental methods in the aforementioned disciplines, to combine
the different methods where necessary, and to apply them to central
questions in theory and practice. Of particular concern was the
further development of freely available open source computer
algebra systems and their interaction in order to create powerful
new computational tools that transcend the boundaries of the
individual disciplines involved. The book covers a broad range of
topics addressing the design and theoretical foundations,
implementation and the successful application of algebraic
algorithms in order to solve mathematical research problems. It
offers a valuable resource for all researchers, from graduate
students through established experts, who are interested in the
computational aspects of algebra, geometry, and/or number theory.
A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.
Originating from a summer school taught by the authors, this
concise treatment includes many of the main results in the area. An
introductory chapter describes the fundamental results on linear
algebraic groups, culminating in the classification of semisimple
groups. The second chapter introduces more specialized topics in
the subgroup structure of semisimple groups, and describes the
classification of the maximal subgroups of the simple algebraic
groups. The authors then systematically develop the subgroup
structure of finite groups of Lie type as a consequence of the
structural results on algebraic groups. This approach will help
students to understand the relationship between these two classes
of groups. The book covers many topics that are central to the
subject, but missing from existing textbooks. The authors provide
numerous instructive exercises and examples for those who are
learning the subject as well as more advanced topics for research
students working in related areas.
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