I am given a set K with some given values and want to show that it is a normal subgroup of An for some given integer n. Is this how i prove it? First prove K is a subgroup of An Second prove that An/K exists and show all its distinct cosets. Therefore K is normal in An. Is that it or do I have to show something else as well or use a contradiction? Thankyou
Prove K is a normal subgroup of An for some integer n
0
$\begingroup$
group-theory
finite-groups
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1The quotient always exists. Normality of $K$ just ensures that the multiplication from $A_n$ carries over to the quotient to make it a group. You should look up the definition of normal. – 2012-10-25
1 Answers
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Show first $K \leq A_n$. Then to show $K \lhd A_n$, you have to prove that $xKx^{-1} \subseteq A_n$ for all $x \in A_n$
$\lhd$ means $K$ is normal subgroup of $A_n$
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1ok$z$ thanks a lot for ur help! – 2012-10-25