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Finite Geometries, Groups, and Computation - Proceedings of the Conference 'Finite Geometries, Groups, and Computation', Pingree Park, Colorado, USA, September 4-9, 2004 (Hardcover)
Alexander Hulpke, Robert Liebler, Tim Penttila, Akos Seress
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R10,298
Discovery Miles 102 980
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Ships in 10 - 15 working days
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This volume is the proceedings of a conference on Finite
Geometries, Groups, and Computation that took place on September
4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State
University). Not accidentally, the conference coincided with the
60th birthday of William Kantor, and the topics relate to his major
research areas. Participants were encouraged to explore the deeper
interplay between these fields. The survey papers by Kantor,
O'Brien, and Penttila should serve to introduce both students and
the broader mathematical community to these important topics and
some of their connections while the volume as a whole gives an
overview of current developments in these fields.
Following an initiative of the late Hans Zassenhaus in 1965, the
Departments of Mathematics at The Ohio State University and Denison
University organize conferences in combinatorics, group theory, and
ring theory. Between May 18-21, 2000, the 25th conference of this
series was held. Usually, there are twenty to thirty invited
20-minute talks in each of the three main areas. However, at the
2000 meeting, the combinatorics part of the conference was
extended, to honor the 65th birthday of Professor Dijen
Ray-Chaudhuri. This volulme is the proceedings of this extension.
Most of the papers are in coding theory and design theory,
reflecting the major interest of Professor Ray-Chaudhuri, but there
are articles on association schemes, algebraic graph theory,
combinatorial geometry, and network flows as well. There are four
surveys and seventeen research articles, and all of these went
through a thorough refereeing process. The volume is primarily
recommended for researchers and graduate students interested in new
developments in coding theory and design theory.
This volume contains contributions by the participants of the
conference "Groups and Computation," which took place at The Ohio
State University in Columbus, Ohio, in June 1999. This conference
was the successor of two workshops on "Groups and Computation" held
at DIMACS in 1991 and 1995. There are papers on permutation group
algorithms, finitely presented groups, polycyclic groups, and
parallel computation, providing a representative sample of the
breadth of Computational Group Theory. On the other hand, more than
one third of the papers deal with computations in matrix groups,
giving an in-depth treatment of the currently most active area of
the field. The points of view of the papers range from explicit
computations to group-theoretic algorithms to group-theoretic
theorems needed for algorithm development.
Permutation group algorithms are indispensable in the proofs of many deep results, including the construction and study of sporadic finite simple groups. This work describes the theory behind permutation group algorithms, up to the most recent developments based on the classification of finite simple groups. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout. The central theme is the description of nearly linear time algorithms, which are extremely fast both in terms of asymptotic analysis and of practical running time. The book fills a significant gap in the symbolic computation literature for readers interested in using computers in group theory.
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