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Fundamental Algorithms for Permutation Groups
Taschenbuch von Gregory Butler
Sprache: Englisch

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Beschreibung
This is the first-ever book on computational group theory.
It provides extensive and up-to-date coverage of the
fundamental algorithms for permutation groups with reference
to aspects of combinatorial group theory, soluble groups,
and p-groups where appropriate.
The book begins with a constructive introduction to group
theory and algorithms for computing with small groups,
followed by a gradual discussion of the basic ideas of Sims
for computing with very large permutation groups, and
concludes with algorithms that use group homomorphisms, as
in the computation of Sylowsubgroups. No background in
group theory is assumed.
The emphasis is on the details of the data structures and
implementation which makes the algorithms effective when
applied to realistic problems. The algorithms are developed
hand-in-hand with the theoretical and practical
[...] algorithms are clearly described,
examples are given, exercises reinforce understanding, and
detailed bibliographical remarks explain the history and
context of the work.
Much of the later material on homomorphisms, Sylow
subgroups, and soluble permutation groups is new.
This is the first-ever book on computational group theory.
It provides extensive and up-to-date coverage of the
fundamental algorithms for permutation groups with reference
to aspects of combinatorial group theory, soluble groups,
and p-groups where appropriate.
The book begins with a constructive introduction to group
theory and algorithms for computing with small groups,
followed by a gradual discussion of the basic ideas of Sims
for computing with very large permutation groups, and
concludes with algorithms that use group homomorphisms, as
in the computation of Sylowsubgroups. No background in
group theory is assumed.
The emphasis is on the details of the data structures and
implementation which makes the algorithms effective when
applied to realistic problems. The algorithms are developed
hand-in-hand with the theoretical and practical
[...] algorithms are clearly described,
examples are given, exercises reinforce understanding, and
detailed bibliographical remarks explain the history and
context of the work.
Much of the later material on homomorphisms, Sylow
subgroups, and soluble permutation groups is new.
Zusammenfassung
This is the first-ever book on computational group theory. It covers the fundamental algorithms for permutation groups, with emphasis on the details of data structures and implementation which make the algorithms effective when applied to realistic problems.
Inhaltsverzeichnis
Group theory background.- List of elements.- Searching small groups.- Cayley graph and defining relations.- Lattice of subgroups.- Orbits and schreier vectors.- Regularity.- Primitivity.- Inductive foundation.- Backtrack search.- Base change.- Schreier-Sims method.- Complexity of the Schreier-Sims method.- Homomorphisms.- Sylow subgroups.- P-groups and soluble groups.- Soluble permutation groups.- Some other algorithms.
Details
Erscheinungsjahr: 1991
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xii
244 S.
ISBN-13: 9783540549550
ISBN-10: 3540549552
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Butler, Gregory
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 15 mm
Von/Mit: Gregory Butler
Erscheinungsdatum: 27.11.1991
Gewicht: 0,394 kg
Artikel-ID: 102135779
Zusammenfassung
This is the first-ever book on computational group theory. It covers the fundamental algorithms for permutation groups, with emphasis on the details of data structures and implementation which make the algorithms effective when applied to realistic problems.
Inhaltsverzeichnis
Group theory background.- List of elements.- Searching small groups.- Cayley graph and defining relations.- Lattice of subgroups.- Orbits and schreier vectors.- Regularity.- Primitivity.- Inductive foundation.- Backtrack search.- Base change.- Schreier-Sims method.- Complexity of the Schreier-Sims method.- Homomorphisms.- Sylow subgroups.- P-groups and soluble groups.- Soluble permutation groups.- Some other algorithms.
Details
Erscheinungsjahr: 1991
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xii
244 S.
ISBN-13: 9783540549550
ISBN-10: 3540549552
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Butler, Gregory
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 15 mm
Von/Mit: Gregory Butler
Erscheinungsdatum: 27.11.1991
Gewicht: 0,394 kg
Artikel-ID: 102135779
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