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How many different non-isomorphic Abelian groups of order 4 are there?

1. 2
2. 3
3. 4
4. 5

Correct answer: 2

Solution

There are two non-isomorphic Abelian groups of order 4: the cyclic group of order 4, denoted as Z₄, and the direct product of two cyclic groups of order 2, denoted as Z₂ × Z₂. These groups have different structures, which makes them non-isomorphic.

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