Explore BrainMass

Explore BrainMass

    Nonisomorphic Central Extensions

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

    Describe all nonisomorphic central extensions of Z_2 x Z_2 by a cyclic group Z_n for arbitrary n, meaning central extensions of the form:

    1 --> Z_n --> G --> Z_2 x Z_2 --> 1

    © BrainMass Inc. brainmass.com March 4, 2021, 5:45 pm ad1c9bdddf

    Solution Preview

    There is a theorem stating that for an extension like this:


    If H is an abelian group then all the extensions can be found through analyzing the second homologies in the form of H^2(M, H).
    We also know that if m and n are relatively prime then Z_m x Z_n= Z_(mxn).
    Well, now we want G such ...

    Solution Summary

    Nonisomorphic central extensions are described.