Let C be the class of finite nilpotent, solvable, symmetric, simple or semi-simple groups and n be a positive integer. We discuss the following question on group laws: What is the length of the shortest non-trivial law holding for all finite groups from the class C of order less than or equal to n?:Introduction
0 Essentials from group theory
1 The two main tools
1.1 The commutator lemma
1.2 The extension lemma
2 Nilpotent and solvable groups
2.1 Definitions and basic properties
2.2 Short non-trivial words in the derived series of F_2
2.3 Short non-trivial words in the lower central series of F_2
2.4 Laws for finite nilpotent groups
2.5 Laws for finite solvable groups
3 Semi-simple groups
3.1 Definitions and basic facts
3.2 Laws for the symmetric group S_n
3.3 Laws for simple groups
3.4 Laws for finite linear groups
3.5 Returning to semi-simple groups
4 The final conclusion
Index
Bibliography / Sei C die Klasse der endlichen nilpotenten, auflösbaren, symmetrischen oder halbeinfachen Gruppen und n eine positive ganze Zahl. We diskutieren die folgende Frage über Gruppengesetze: Was ist die Länge des kürzesten nicht-trivialen Gesetzes, das für alle endlichen Gruppen der Klasse C gilt, welche die Ordnung höchstens n haben?:Introduction
0 Essentials from group theory
1 The two main tools
1.1 The commutator lemma
1.2 The extension lemma
2 Nilpotent and solvable groups
2.1 Definitions and basic properties
2.2 Short non-trivial words in the derived series of F_2
2.3 Short non-trivial words in the lower central series of F_2
2.4 Laws for finite nilpotent groups
2.5 Laws for finite solvable groups
3 Semi-simple groups
3.1 Definitions and basic facts
3.2 Laws for the symmetric group S_n
3.3 Laws for simple groups
3.4 Laws for finite linear groups
3.5 Returning to semi-simple groups
4 The final conclusion
Index
Bibliography
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:36487 |
| Date | 07 December 2019 |
| Creators | Schneider, Jakob |
| Contributors | Thom, Andreas, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/updatedVersion, doc-type:masterThesis, info:eu-repo/semantics/masterThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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