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Show that if every element in a group is its own inverse, then the group must be abelian.

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: Dec 2013

1 Answer
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Let a, b ∈ G.

So we have a1=a and b1=b.

Also a • b ∈ G, therefore ab=(a.b)1=b1a1=ba.

So we have a • b = b • a,

Hence, G is abelian.

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