Properties of a group question.

[gottfried]

Suppose G is a group and g,h are elements of g.

Does (g.h)ⁿ=gⁿ.hⁿ if we don't know what the groups operation is.

 

[HallsofIvy]

In general, no. (gh)²= (gh)(gh) which, in a general group, is not the same as (gg)(hh)= g²h². Of course, in a "commutative" group that would be true.

 

[gottfried]

That is actually really obvious should have thought about it a little harder.

Thanks for the help.