Number of orbits under automorphism group: Difference between revisions
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==Definition== | ==Definition== | ||
Let <math>G</math> be a [[group]]. The '''number of orbits under automorphism group''' of <math>G</math> is the number of [[orbit]]s of the set <math>G</math> under the action of the [[automorphism group]] <math>\operatorname{Aut}(G)</math>. | Let <math>G</math> be a [[group]]. The '''number of orbits under automorphism group''' or '''number of automorphism classes''' of <math>G</math> is the number of [[orbit]]s of the set <math>G</math> under the action of the [[automorphism group]] <math>\operatorname{Aut}(G)</math>. | ||
==Facts== | |||
* [[Number of orbits of irreducible representations equals number of orbits under automorphism group]] (true for a [[finite group]] and a [[splitting field]] thereof) | |||
Revision as of 18:40, 20 July 2011
Definition
Let be a group. The number of orbits under automorphism group or number of automorphism classes of is the number of orbits of the set under the action of the automorphism group .