# Math Help - showthat...

1. ## showthat...

a) in every group G, for all a,b members of G, and for all n member of Z(integers): (a^-1 * b * a)^n= a^-1 * b^n * a

(Do you have to use induction for this, because i think you do, but i am unsure?)

b) Every group table for a finite group is a Latian square, that is, each element of the group appears exactly once in each row and each column.

2. Originally Posted by mandy123
a) in every group G, for all a,b members of G, and for all n member of Z(integers): (a^-1 * b * a)^n= a^-1 * b^n * a
Just look at what happens: $(a^{-1} ba)^n = (a^{-1} ba)(a^{-1} ba)(a^{-1} ba) .... = a^{-1} b(aa^{-1})b(aa^{-1}) ... a= a^{-1} b^n a$

b) Every group table for a finite group is a Latian square, that is, each element of the group appears exactly once in each row and each column.
Hint: The equation $ax=b$ always a solution in a group.