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definition:order_for_groups
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definition:order_for_groups [2013/08/21 09:16] joshuawiscons created |
definition:order_for_groups [2013/08/21 12:58] (current) bmwoodruff |
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| Let $G$ be a [[definition: | Let $G$ be a [[definition: | ||
| * The $\textdef{order}$ of $G$, denoted $|G|$, is the cardinality of $G$. | * The $\textdef{order}$ of $G$, denoted $|G|$, is the cardinality of $G$. | ||
| - | * The $\textdef{order}$ of $g$, denoted $|g|$, is the smallest positive integer $n$ such that $g^n = e$, if such an $n$ exists. If no such $n$ exists, $g$ is said to have infinite order. | + | * The $\textdef{order}$ of $g$, denoted $|g|$, is the smallest positive integer $n$ such that $g^n = e$, if such an $n$ exists. If no such $n$ exists, |
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| - | {{tag> | + | {{tag> |
definition/order_for_groups.1377090998.txt.gz · Last modified: 2013/08/21 09:16 by joshuawiscons
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