Difference between revisions of "Normal subgroup"

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Revision as of 18:33, 13 May 2015

Definition

Let [ilmath](G,\times)[/ilmath] be a group and [ilmath]H[/ilmath] a subgroup of [ilmath]G[/ilmath], we say [ilmath]H[/ilmath] is a normal subgroup[1] of [ilmath]G[/ilmath] if:

  • [math]\forall x\in G[xH=Hx][/math] where the [ilmath]xH[/ilmath] and [ilmath]Hx[/ilmath] are left and right cosets


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References

  1. ↑ Undergraduate Algebra - Serge Lang
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