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SchlieBlich stellte sich heraus, d Gruppen in Kunst und Wissenschaft tiberhaupt eine wichtige Rolle spielen. Die Bedeutung der Gruppen ergibt sich aus ihrem Nutzen flir das Studium von Symme- trien, wie wir in Kapitel 7 sehen werden. Symmetrie tritt in der Natur sehr Mufig auf, und wo immer Symmetrie auf tritt, gibt es eine entsprechende Gruppe. Aus diesem Grund findet die Gruppentheorie in vielen WissenschaftenAnwendung. Sie wird z. B. von Kri- stallographen beim Studium von Symmetrien der Kristalle von Mineralen verwendet. Sie wird ebenso von Physikem und Chemikem bei Untersuchungen von Symmetrien von Elementarteilchen und Kraftefeldem benutzt. Die Bedeutung der Gruppentheorie wurde erst kiirzlich sehr nachdriicklich unterstrichen, als einige Physiker mit Hilfe der Gruppen- theorie die Existenz eines Elementarteilchens voraussagten, das nie zuvor beobachtet worden war, und die Eigenschaften beschrieben, die es haben sollte. 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