If K is a normal subgroup of G has index m, show that g^m belongs to K for all g belonging to G.© BrainMass Inc. brainmass.com March 4, 2021, 5:52 pm ad1c9bdddf
Proof. Since K is a normal subgroup of G has index m, we have
for all x belonging to G. So, ...
A proof involving subgroups and indicies is offered. The proof is concise.