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 justification.All 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 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.

Klappentext

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
justification.All 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.

Inhalt
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.

Produktinformationen

Titel:	Fundamental Algorithms for Permutation Groups
Autor:	Gregory Butler
EAN:	9783540549550
ISBN:	3540549552
Format:	Kartonierter Einband
Herausgeber:	Springer Berlin Heidelberg
Anzahl Seiten:	256
Gewicht:	394g
Größe:	H235mm x B155mm x T13mm
Jahr:	1991
Untertitel:	Englisch
Auflage:	1991