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Nonisomorphic Central Extensions

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

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.