Key to "Let H={σ∈S5∣σ94)=4} Show that H≤S5"

College
Algebra
Abstract algebra

Aneeka Hunt

Answered question

2021-01-31

Let

H = {σ \in S_{5} ∣ σ 94) = 4}

Show that

H \leq S_{5}

Answer & Explanation

Roosevelt Houghton

Skilled2021-02-01Added 106 answers

$σ$ is bijective map from ${1, 2, 3, 4, 5} \to {1, 2, 3, 4, 5}$
but $σ (4) = 4$
$σ$ is bijective map from ${1, 2, 3, 4, 5} \to {1, 2, 3, 4, 5}$
If $f, g \in H$
$f g^{- 1} (4) = f (g^{- 1} (4)) = f (4) = 4$
$f g^{- 1} (4) = 4$
$f g^{- 1} \in H$

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