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Show that if every element in a group is its own inverse, then the group must be abelian.
1 Answer
written 8.2 years ago by |
Let (G,o) is a group.
∴ if a,b∈G then a−1,b−1∈G
also if aob∈G the (aob)−1∈G
But we have a=a−1 and b=b−1
As such (aob)=(aob)−1=b−1oa−1=(boa)
i.e, (G,o) is commutative. Hence (G,o) is abelian.