- #1
basil32
- 11
- 0
Homework Statement
If x and g are elements of the group G, prove that |x|=|g-1xg|. Deduce that |ab| =|ba| for all a,b [itex]\in[/itex] G
Homework Equations
The Attempt at a Solution
I've written a proof but does not seem quite right:
if (g-1xg)n= xm then n must be equal m
g-nxngn = xm then
xngn =gnxm
xn =gnxmg-n
xm =g-nxngn
xn = gn(g-nxmgn)g-n
xn = xm
n = m