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    Nonisomorphic Central Extensions

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    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

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    https://brainmass.com/math/linear-algebra/nonisomorphic-central-extensions-9446

    Solution Preview

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

    1-->H-->G-->M-->1

    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.

    $2.49

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