SOLUTION: Give an example of a group of size four, acting on a set of size four. And describe its orbits and stabilizers.
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Question 865859: Give an example of a group of size four, acting on a set of size four. And describe its orbits and stabilizers.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
For example, let 
(that is, the elements of G are 1, x, x^2, x^3 with x^4 = 1), and suppose G acts on 
. Then, for 
,
 = \{ gk | g \in G \})
 = \{ g \in G: gk = k \})
It follows that for all ,  = \{1, x, x^2, x^3 \})
and  = \{1\})
.
This satisfies the orbit-stabilizer theorem  \cdot Stab(k) = |G|)
for 
.
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