Internal semidirect product: Difference between revisions
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* <math>N</math> is a [[normal subgroup]] of <math>G</math> | * <math>N</math> is a [[normal subgroup]] of <math>G</math> | ||
* <math>N</math> and <math>H</math> are [[permutable | * <math>N</math> and <math>H</math> are [[permutable complements]] | ||
Note here that <math>H</math> acts as [[automorphism]]s on <math>N</math> by the conjugation action. | Note here that <math>H</math> acts as [[automorphism]]s on <math>N</math> by the conjugation action. | ||
Revision as of 16:50, 13 December 2007
This article describes a product notion for groups. See other related product notions for groups.
This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
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Definition
Definition with symbols
A group is termed an internal semidirect product of subgroups and if the following hold:
- is a normal subgroup of
- and are permutable complements
Note here that acts as automorphisms on by the conjugation action.