Die Theorie Der Gruppen Von Endlicher Ordnung: Mit Anwendungen Auf Algebraische Zahlen Und Gleichungen Sowie Auf Die Kristallographie
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I. Zur Vorgeschichte der Gruppentheorie . . . . . . . 1 II. Ableitung des Gruppenbegriffs aus den Permutationen 4 1. Kapitel. Die Grundlagen. 1. Die Postulate des Gruppenbegriffs 10 2. Die Gruppentafel 12 3. Untergruppen . . . . 14 4. Zyklische Gruppen . . 16 5. Beispiele von Gruppen 20 6. Elementenkomplexe 25 2. Kapitel. Normalteiler und Faktorgruppen. 7. Normalteiler. . . 28 8. Faktorgruppen. . . . . . . . . 31 9. Isomorphe Gruppen. . . . . . . 33 10. Der Hauptsatz tiber Normalteiler . 35 11. Kompositionsreihen. 38 12. Hauptreihen. . . . . . . 40 13. Kommutatorgruppen . . . 43 14. Ein Theorem von Frobenius 44 3. Kapitel. Abelsche Gruppen. 15. Basis einer Abelschen Gruppe . . . . . . . . . . . . . 46 16. Die Invarianten einer Abelschen Gruppe. . . . . . . . . 50 17. Untergruppen und Faktorgruppen einer Abelschen Gruppe. 52 18. Die Galoisfelder und Reste nach Primzahlpotenzen 54 19. Existenz der Galoisfelder . . . . . . . . . . . . . . . 57 4. Kapitel. Konfugierte Untel'gl'uppen. 20. Normalisatoren . . . . . . . . . . . . . 61 21. Zerlegung einer Gruppe nach zwei Untergruppen 62 5. Kapitel. Sylowgl'uppen und p-Gruppen. 22. Sylowgruppen ........ . 64 23. Norrnalisatoren der Sylowgruppen . . . . . . . 66 Inhaltsverzeichnis. x 24. Gruppen. deren Ordnung eine Primzahlpotenz ist 69 25. Spezielle p-Gruppen . . . . . . 71 6. Kapitel. S ymmetrien del' Ornamente. 26. Vorbemerkungen. . 76 27. Die ebenen Gitter 76 28. Die Streifenornamente 80 29. Die Flachenornamente 85 30. Beispiele von Fiachenornamenten 91 31. Die Bewegungsgruppen der Ebene mit endlichem Fundamentalbereich 95 7. Kapitel. Die Krystallklassen. 32. Die Raumgitter . . 98 102 33. Die Krystallklassen . 8. Kapitel. Permutationsgruppen.
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