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simple examples
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]] (''G'',<math>\cdot</math>) is called a '''subgroup''', if (''H'',<math>\cdot</math>) is itself a group.
==Simple Examples==
# <math>(2\mathbb{Z},+)</math> is a subgroup of <math>(\mathbb{Z},+) </math>
# <math>(\mathbb{Z},+) </math> is a subgroup of <math>(\mathbb{Q},+) </math>
# <math>(\mathbb{Q}^+,\cdot) </math> is a subgroup of <math>(\mathbb{R}^+,\cdot) </math>
[[Category:Algebra]]
[[Category:Algebra]]