Group Theory 42, Converse of Lagrange Theorem is False

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Group Theory 42, Converse of Lagrange Theorem is False
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Why the distinct a*2 s are exactly nine ?

uttiyadas
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At 5:48 how did you prove that H is a subgroup of G implies that H is a normal subgroup of G?

JohnSmith-utth
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why a^2 H = H is true for all a in A_4 ?

fawzyhegab