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'proper subgroup'
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| Title of object: |
proper subgroup |
| Canonical Name: |
ProperSubgroup |
| Type: |
Definition |
| Created on: |
2002-06-27 19:44:33 |
| Modified on: |
2002-06-28 05:58:52 |
| Classification: |
msc:20A99 |
| Defines: |
proper subgroup, improper subgroup |
Revision comment (for changes between this and next version):
Preamble:
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\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
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%\usepackage{amsthm}
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%\usepackage{xypic}
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Content:
A group $H$ is a \emph{proper subgroup} of a group $G$ if and only if $H$ is a subgroup of $G$ and \begin{equation}H \neq G.\end{equation}
Similarly a group $H$ is an \emph{improper subgroup} of a group $G$ if and only if $H$ is a subgroup of $G$ and \begin{equation}H=G.\end{equation} |
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