Question

Prove that an Abelian group with two elements of order 2 must have a subgroup of order four.
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Answer 1

Answer:

Prove that an abelian group with two elements of order 2 must have a subgroup of order 4. Solution. ... Since H ∩K is a subgroup of both H and K, it follows by Lagrange's theorem that |H ∩ K| must divide both |H| = 15 and |K| = 28. Since 15 and 28 are relatively prime, we again conclude that |H ∩ K| = 1.

Step-by-step explanation:

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