SUMMARY
The order of the permutation (1 2)(3 4) in the symmetric group S_4 is 2. This conclusion is reached by calculating the product of the permutation with itself: (1 2)(3 4)(1 2)(3 4), which results in the identity permutation (1)(2)(3)(4). Thus, the order is confirmed to be 2.
PREREQUISITES
- Understanding of permutation notation in group theory
- Familiarity with the symmetric group S_n
- Knowledge of the concept of order of a permutation
- Basic algebraic manipulation of permutations
NEXT STEPS
- Study the properties of symmetric groups, specifically S_4
- Learn about cycle notation and its applications in group theory
- Explore the concept of the order of elements in abstract algebra
- Investigate the relationship between permutations and group operations
USEFUL FOR
Students of abstract algebra, mathematicians interested in group theory, and anyone studying permutations and their properties.