Explore BrainMass
Share

Explore BrainMass

    Groups and Subgroups : Indicies

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 October 9, 2019, 3:53 pm ad1c9bdddf
    https://brainmass.com/math/group-theory/groups-and-subgroups-indicies-15973

    Solution Preview

    Proof. Since K is a normal subgroup of G has index m, we have
    xK=Kx
    for all x belonging to G. So, ...

    Solution Summary

    A proof involving subgroups and indicies is offered. The proof is concise.

    $2.19