- #1
PsychonautQQ
- 784
- 10
say K is normal in G hence we have a factor group G/K.
let g be an element of G where |g| = n.
so Kg^n = K since g^n = 1.
and using the properties of factor groups, we know Kg^n = (Kg)^n
hence (Kg)^n = K
So we know that the order of Kg divides n.
Is this correct thinking? Factor groups are trippin me out
let g be an element of G where |g| = n.
so Kg^n = K since g^n = 1.
and using the properties of factor groups, we know Kg^n = (Kg)^n
hence (Kg)^n = K
So we know that the order of Kg divides n.
Is this correct thinking? Factor groups are trippin me out