Exercise · ZW-ORDER-OF-A-GROUP-010 · ★★★ Advanced
In \(S_3\), how many permutations of \(\{1,2,3\}\) fix the element \(1\)?
Choose one option.
Show answer
- B. 2
Explanation
With 1 fixed, only 2 and 3 can be permuted: the identity and the swap of 2 and 3. That is 2 of the 6 permutations.
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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