< G × H,*> is a group with identity (eg, eH).
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Transcribed Image Text:3. Let < G,*1> and < H,*2> be two groups with identity elements eg and en· As you know the
product of G and H is defined as:
G x H = {(a,b)|a E G,b E H}
Define an operation * on G × H as follows:
(a, b) * (a', b') = (a *1 a', b *2 b') , where (a, b), (a', b') E G × H.
Prove that < G × H,*> is a group with identity (eg, eH).
4. Prove that if G is abelian then H = {h E G|h¯1 = h} is a subgroup of the group G.
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