Fundamental Algorithms for Permutation Groups [1 ed.] 3540549552, 9783540549550, 0387549552
This is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of the fundamen
204 96 1MB
English Pages 244 [250] Year 1991
Table of contents :
Introduction....Pages 1-6
Group theory background....Pages 7-13
List of elements....Pages 14-23
Searching small groups....Pages 24-32
Cayley graph and defining relations....Pages 33-43
Lattice of subgroups....Pages 44-55
Orbits and schreier vectors....Pages 56-63
Regularity....Pages 64-70
Primitivity....Pages 71-77
Inductive foundation....Pages 78-97
Backtrack search....Pages 98-116
Base change....Pages 117-128
Schreier-Sims method....Pages 129-142
Complexity of the Schreier-Sims method....Pages 143-155
Homomorphisms....Pages 156-170
Sylow subgroups....Pages 171-183
P-groups and soluble groups....Pages 184-204
Soluble permutation groups....Pages 205-228
Some other algorithms....Pages 229-232
Introduction....Pages 1-6
Group theory background....Pages 7-13
List of elements....Pages 14-23
Searching small groups....Pages 24-32
Cayley graph and defining relations....Pages 33-43
Lattice of subgroups....Pages 44-55
Orbits and schreier vectors....Pages 56-63
Regularity....Pages 64-70
Primitivity....Pages 71-77
Inductive foundation....Pages 78-97
Backtrack search....Pages 98-116
Base change....Pages 117-128
Schreier-Sims method....Pages 129-142
Complexity of the Schreier-Sims method....Pages 143-155
Homomorphisms....Pages 156-170
Sylow subgroups....Pages 171-183
P-groups and soluble groups....Pages 184-204
Soluble permutation groups....Pages 205-228
Some other algorithms....Pages 229-232
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