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Leta and b be elements of odd order in a group. Show that .512 and b2 commute if and only if a and b commute. Also show that this does not have to hold if a and b have even order.

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Leta and b be elements of odd order in a group. Show that .512 and b2 commute
if and only if a and b commute. Also show that this does not have to hold if a and b
have even order.

 
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