document.write( "Question 1205501: Express each of the given permutation of [ 1 2 3 4 5 6 7 8 ] as a product of disjoint cycles.
\n" ); document.write( " [1 2
\n" ); document.write( " 3 6
\n" ); document.write( " 3 4
\n" ); document.write( " 4 5
\n" ); document.write( " 5 6
\n" ); document.write( " 1 7
\n" ); document.write( " 7 8 8 2 ]\r
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Algebra.Com's Answer #847961 by CPhill(1959)\"\" \"About 
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To express a permutation as a product of disjoint cycles, we follow these steps:\r
\n" ); document.write( "\n" ); document.write( "1. **Start with an element:** Choose any element, say 1.
\n" ); document.write( "2. **Trace its cycle:** Follow the permutation to see where 1 goes. 1 goes to 2, 2 goes to 8, 8 goes to 7, 7 goes to 1. So, we have the cycle (1 2 8 7).
\n" ); document.write( "3. **Choose an unused element:** Choose an element not in the previous cycle, say 3.
\n" ); document.write( "4. **Trace its cycle:** 3 goes to 6, 6 goes to 5, 5 goes to 4, 4 goes to 3. So, we have the cycle (3 6 5 4).\r
\n" ); document.write( "\n" ); document.write( "Since all elements are now included in cycles, we have expressed the permutation as a product of disjoint cycles: \r
\n" ); document.write( "\n" ); document.write( "**(1 2 8 7)(3 6 5 4)**
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