Re: Groups and Inverse order

[Virgil]

In article <1122746633.067740.56910@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
 "ADH" <adoug48@xxxxxxxxxxx> wrote:

> Hi all,
> 
> I'm trying to solve the following problem on groups.
> a,) Let G be a group.  If a belongs to G, then the order of a is the
> same as the order of its inverse.

Compare (a^n)^(-1) to (a^(-1))^n

> b.) Let G be a group.  Let a,b belong to G.  Show that a and b have the
> same order if b=g^(-1)ag, for some element g belonging to G.

Consider b^n = (g^(-1)ag)^n versus g^(-1)a^(-1)g