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Verizon [17]
3 years ago
14

Find a normal subgroup of v which is not normal in a4.

Mathematics
1 answer:
Tpy6a [65]3 years ago
6 0

he elements of the Klein <span>44</span>-group sitting inside <span><span>A4</span><span>A4</span></span> are precisely the identity, and all elements of <span><span>A4</span><span>A4</span></span>of the form <span><span>(ij)(kℓ)</span><span>(ij)(kℓ)</span></span> (the product of two disjoint transpositions).

Since conjugation in <span><span>Sn</span><span>Sn</span></span> (and therefore in <span><span>An</span><span>An</span></span>) does not change the cycle structure, it follows that this subgroup is a union of conjugacy classes, and therefore is normal.

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