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    Central Extension Problem

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    Find a nontrivial central extension

    1 --> Z_2 --> G --> A_4 --> 1

    meaning determine a group G. Is it unique?
    (You may use the fact that A_4 has a normal series Z_2 x Z_2/Z3)

    © BrainMass Inc. brainmass.com November 24, 2022, 11:36 am ad1c9bdddf

    Solution Preview

    We consider G= Z_6 x A_4/Z_3 where Z_3 is a subgroup of Z_6 x A_4 which defines a 1 to 1 homomorphism map shown as a--->(a,a).
    Now, we can define 1--->Z_2--->G--->A_4--->1 as a central extension if we assume that ...

    Solution Summary

    A central extension problem is solved. The nontrivial central extension functions are determined.