Subgroup
In group theory, a branch of mathematics, given a group [math]\displaystyle{ G }[/math] under a binary operation, a subset [math]\displaystyle{ H }[/math] of [math]\displaystyle{ G }[/math] is called a subgroup of [math]\displaystyle{ G }[/math] if the elements [math]\displaystyle{ H }[/math] also forms a group under the binary operation.
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Group theory
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The situation could arise in which the subset [math]\displaystyle{ H }[/math] does not comply with the binary operation.