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
Follow Math Help Forum on Facebook and Google+
Originally Posted by Coda202 Show that Ng is a subgroup of G. Just check the definitions of being a subgroup. Prove that, |Sg| = |G/Ng| and that {Sg|g in G} is a partition of G Hint: iff iff .
View Tag Cloud