Exercise · ZW-ORDER-OF-A-GROUP-004 · ★☆☆ Basic
The group of units mod 12, \(\{x : \gcd(x,12)=1\}\) under multiplication mod 12, has order
Choose one option.
Show answer
- B. 4
Explanation
The residues coprime to 12 are \(1,5,7,11\), four in all; that is, \(\varphi(12)=4\).
Review the concept: Order of a group
The order of a finite group \(G\) is its number of elements; if \(G\) is infinite it has infinite order.
\[|G|\]
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