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Sometimes your computer may display an error stating that the kernel is a group action. This problem can be caused by a number of reasons.

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The kernel using the action is to find all the elements of the group that improve everything in S: Ker φ = φ (g) corresponds to e = s. Φ (g) = s to get all s ∈ S.

Show that the kernel through the group action of $ G $, working with the set $ A $, actually corresponds to the kernel of the same permutation representation of this action.

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I have exhausted myself with this definition, because ideallyI know a definition related to the kernel of a homomorphism, essentially $ g in G ~ $ (elements of the area in which the image identifies the Target Group)

How does this standard apply to the $ f: G times A to A $ map, where the set is the primary target domain?

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applied Jun 13, 2016 at 8:08 pm

## What is the action of a group?

A numeric action is the representation that these group members are treated as set symmetries. Many groups, by design, receive natural group action; For example, Diedergemeinschaft D 4 D_4 D4 acts in relation to the corner points of the square due to the group, like any kind of set of symmetries of the corresponding square.

## What is the stabilizer of a group?

Support s is a set Gs = g∈G∣g⋅s = s, a set of G elements that leave s unchanged for your current action. For example, a coin flip stabilizer is a value created by permutations of positive signs.

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## Not The Answer You’re Looking For? Explore, Among Other Questions, Describe The Group’s Activity On Group Theory, Or Ask Your Own Question.

The action is based on the parameter $ K = g in G; g cdot any = a, forall in every A $. Now the corresponding permutation reflectivity is a homomorphism of the group $ psi: G to s_a $, given by $ psi (g) (a) = g cdot this $.

- $ K substeq ker psi $

Let $ k in K $, then for all $ a in A $ it is preserved that $ psi (k) (a) K = cdot a is equal to a $, therefore $ psi (k) means id_A $, then $ k in ker psi $.

Enjoy a fasterKarnan I En Gruppatgard

Nocciolo Di Un Azione Di Gruppo

Kern Einer Gruppenaktion

그룹 작업의 커널

Kern Van Een Groepsactie

Noyau D Une Action De Groupe

Jadro Akcji Grupowej

Nucleo De Una Accion Grupal

Yadro Gruppovogo Dejstviya

Nucleo De Uma Acao De Grupo