Subgroup test: Difference between revisions

Revision as of 19:00, 29 May 2007

Revision as of 16:07, 29 June 2007

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Or more formally let <math>G\,</math> be a group and let <math>H\,</math> be a nonempty a subset of <math>G\,</math>. If <math>\forall{ a, b \in H}, ab^{-1} \in H</math> then <math>H\,</math> is a subgroup of <math>G\,</math>.

A corollary of this theorem is the two-step subgroup test which statestates that a nonempty subset of a group is itself a group if the subset is [[Closure (mathematics)|closed]] under the operation as well as under the taking of inverses.

=Proof=