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Let A and B be groups, and consider the product group G=A x B. (a) Prove that...

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Advance Math

Let A and B be groups, and consider the product group G=A xB.

(a) Prove that N={(ea,b) E A x B| b E B} is asubgroup.

(b) Prove that N is isomorphic to B

(c) Prove that N is a normal subgroup of G

(d) Prove that G|N is isomorphic to A

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