Subgroup
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A subgroup [ilmath](H,\times_H:H\times H\rightarrow H[/ilmath] of a Group [ilmath](G,\times_G:G\times G\rightarrow G)[/ilmath] is a set [ilmath]H\subseteq G[/ilmath] which is a group under the operation [ilmath]\times_G[/ilmath] restricted to [ilmath]H\times H[/ilmath].
Definition
Given a group [ilmath](G,\times_G:G\times G\rightarrow G)[/ilmath] we say [ilmath](H,\times_H:H\times H\rightarrow H)[/ilmath] is a subgroup of [ilmath](G,\times_G)[/ilmath] if:
