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Word Metric
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Geliefert zwischen Mi., 28.01.2026 und Do., 29.01.2026
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High Quality Content by WIKIPEDIA articles! In group theory, a word metric on a group G is a way to measure distance between any two elements of G. As the name suggests, the word metric is a metric on G, assigning to any two elements g, h of G a distance d(g,h) that measures how efficiently their difference g 1h can be expressed as a word whose letters come from a generating set for the group. The word metric on G is very closely related to the Cayley graph of G: the word metric measures the length of the shortest path in the Cayley graph between two elements of G. A generating set for G must first be chosen before a word metric on G is specified. Different choices of a generating set will typically yield different word metrics. While this seems at first to be a weakness in the concept of the word metric, it can be exploited to prove theorems about geometric properties of groups, as is done in geometric group theory.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131185809
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131185809
- Format Fachbuch
- Titel Word Metric
- Herausgeber Betascript Publishing
- Anzahl Seiten 92
- Genre Mathematik
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