# 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)

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##### Solution Summary

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

##### 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 ...

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