How many permutations are there in S10?

2! )3! )2! = 5,040 Answer: the number of permutations of order 6 in S10 is 584,640.

What is the maximum order of an element in A10?

21
Maximum order of an element of A10: By considering all possible partitions of 10, we see that the maximum order is 21 (product of a 7-cycle and a 3-cycle).

Does S10 have an element of order 30?

If σ ∈ S10, we can express σ as a product of disjoint cycles σ1 ···σt of lengths k1,k2,…,kt (ki ≥ 2) where k1 + ···kt ≤ 10. We see that the highest possible order is 30 and this is achieved by the product of a 2-cycle, a 3-cycle and a 5-cycle; eg. (12)(345)(678910).

How do you find the order of permutations?

Orders of permutations are determined by least common multiple of the lengths of the cycles in their decomposition into disjoint cycles, which correspond to partitions of 7. Therefore the orders of elements in S7 are 1, 2, 3, 4, 5, 6, 7, 10, 12 and the orders of elements in A7 are 1, 2, 3, 4, 5, 6, 7.

What is the maximum possible order of a permutation in S8?

Answer: (1, 2, 3, 4, 5, 6)(5, 6, 7, 8) = (1, 2, 3, 4, 5)(6, 7, 8) has order 15. 5. (10 points) Find the maximum possible order for an element of S8 and give an example of an element with this order. Explain your answer.

What is maximum order of elements of alternating group A8?

Note that A8 consists of only even permutations and hence the maximum order of any element of A8 can be 15 which is a small number so it’s not that hard to check for each number between 1 and 15 that whether there exists an element of that order or not.

What is the largest order of a permutation in S9?

This discussion on Find the largest order of a permutation in a symmetric group S9. Correct answer is ’20’.

What is the highest order of an element in S9?

lr· The order of an element of cycle type (ll,”” lr) is the lowest common multiple lcm(h, .. ·, lr) of the cycle lengths. Now we can compute for S9 as follows. If r = 1 the maximum order is 9 (corresponding to a single 9-cycle). If r = 2 and h = 2 then the maximum order is 14 = 2·7 for cycle type (2,7).

Does order matter in permutations?

If the order doesn’t matter then we have a combination, if the order do matter then we have a permutation. One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: P(n,r)=n!

What is the order of the permutation group?

The order of a group (of any type) is the number of elements (cardinality) in the group. By Lagrange’s theorem, the order of any finite permutation group of degree n must divide n! since n-factorial is the order of the symmetric group Sn.