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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.
Note (g^n)^(-1) = (g^(-1))^n. Use induction if you need to prove it.
> 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.
Note (g^(-1)ag)^n = g^(-1)a^ng. Use induction again if necessary. Also
note a = (g^(-1))^(-1)b(g^(-1).
> c.) Let G be a group. Show that ab and ba have the same order.
Use (b)
[...]
--
Paul Sperry
Columbia, SC (USA)
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