14 lines
740 B
TeX
14 lines
740 B
TeX
\section{Terminology and Notation}
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\begin{definition}[Order of a Group]
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The number of elements of a group (finite or infinite) is called its \textit{order}. We will use $\abs{G}$ to denote the order of $G$.
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\end{definition}
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\begin{definition}[Order of an Element]
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The \textit{order} of an element $g$ in a group $G$ is the smallest positive integer $n$ such that $g^n = e$. (In additive notation, this would be $ng = 0$.) If no such integer exists, we say that $g$ has \textit{infinite order}. The order of an element $g$ is denoted by $\abs{g}$.
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\end{definition}
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\begin{definition}[Subgroup]
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If a subset $H$ of a group $G$ is itself a group under the operation of $G$, we say that $H$ is a \textit{subgroup} of $G$.
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\end{definition}
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