Difference between revisions of "Subgroup"
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BRichtigen (talk | contribs) (simple examples) |
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| − | A [[subset]] ''H'' of a [[group]] (''G'',<math>\cdot</math>) is called a '''subgroup''', if (''H'',<math>\cdot</math>) is itself a group. | + | A [[subset]] ''H'' of a [[Group (mathematics)|group]] (''G'',<math>\cdot</math>) is called a '''subgroup''', if (''H'',<math>\cdot</math>) is itself a group. |
==Simple Examples== | ==Simple Examples== | ||
# <math>(2\mathbb{Z},+)</math> is a subgroup of <math>(\mathbb{Z},+) </math> | # <math>(2\mathbb{Z},+)</math> is a subgroup of <math>(\mathbb{Z},+) </math> | ||
Latest revision as of 21:10, November 17, 2008
A subset H of a group (G,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cdot} ) is called a subgroup, if (H,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cdot} ) is itself a group.
Simple Examples
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2\mathbb{Z},+)} is a subgroup of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\mathbb{Z},+) }
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\mathbb{Z},+) } is a subgroup of
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\mathbb{Q}^+,\cdot) } is a subgroup of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\mathbb{R}^+,\cdot) }
