How many elements does the center of (ℤ_12,+) have?

Exercise · ZW-CENTER-OF-A-GROUP-002 · ★☆☆ Basic

How many elements does the center of \((\mathbb{Z}_{12},+)\) have?

Choose one option.

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In an abelian group every element commutes with every other, so the center is the whole group, with 12 elements.

The center of a group \(G\) is the set \(Z(G)\) of elements of \(G\) that commute with every element of \(G\).

\[Z(G)=\{\,z\in G : zg=gz\ \text{for all } g\in G\,\}\]