Let G be a finite group with g in G.
Ng, the centralizer of g in G is defined to be the set = {x|xgx^-1 = g}
Show that Ng is a subgroup of G.
Now, letting Sg = {xgx^-1|x in G}
Prove that, |Sg| = |G/Ng|
and that {Sg|g in G} is a partition of G
Let G be a finite group with g in G.
Ng, the centralizer of g in G is defined to be the set = {x|xgx^-1 = g}
Show that Ng is a subgroup of G.
Now, letting Sg = {xgx^-1|x in G}
Prove that, |Sg| = |G/Ng|
and that {Sg|g in G} is a partition of G