Can someone help me with this proof?
Let H be a subgroup of G with index 2.
Prove that g² ∈ H for all g ∈ G.
Thanks!
In a factor group the group operation is defined to be . As long as H is normal, this is well defined and is a group.
You are given that
By Lagrange's theorem since any element of G/H must have order dividing 2, so in this case since .
This means as desired.