Explore BrainMass
Share

Explore BrainMass

    Modern/Abstract Algebra Problem (Group Theory)

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

    What are the normal subgroups in S_4?

    I would appreciate it if someone could also give a thourough explanation of how they came up with the answer.

    © BrainMass Inc. brainmass.com October 9, 2019, 3:36 pm ad1c9bdddf
    https://brainmass.com/math/group-theory/modern-abstract-algebra-problem-group-theory-8419

    Solution Preview

    Please see the attached document.

    Solution. Set of permutations {1,2,3,4} with product operation of composition forms a group. Order of S4 is n*(n-1)*...*2.1=24 elements.

    Permutation types of {1,2,3,4} are

    Four 1 cycles (1)(2)(3)(4) identity 12341234 4!/(1^4*4!)=1 g1
    One 2 cycle (12)(3)(4) transposition ...

    Solution Summary

    Normal subgroups are determined for modern/abstract ground theory. .

    $2.19