Step 1 : If you have a k k cycle τ τ in Sn S n then, what can you say about the number of elements in the centralizer of τ τ ? Answer: k ⋅ (n − k)! k (n k)! is the number of elements in the …

4 For more detail you can see this paper. The maximum order of an element of finite symmetric group by William Miller, American Mathematical Monthly, page 497-506.

Aug 29, 2013 · The order of an element of Sn S n is the least common multiple of the size of its cycles. So if n n is a prime power, then the only way this is possible is if one cycle is of length …

May 17, 2021 · Show that every element of Sn S n can be written as a product of transpositions of the form (1i) (1 i), for various i i. I have proved by induction that if n ≥ 2 n ≥ 2, then every …

The Maximum possible order for an element Sn S n [duplicate] Ask Question Asked 13 years, 2 months ago Modified 8 years, 2 months ago

Mar 15, 2018 · Suppose Sn S n acts on a set of k k element subsets of {1, …, n} {1,, n}, by σ ⋅ {a1, …,ak} = {σ(a1), …, σ(ak)} σ {a 1,, a k} = {σ (a 1),, σ (a k)} where k <n k <n and σ ∈Sn σ ∈ …

Jan 25, 2012 · 14 For a finite group, there is a perfectly systematic way: to find the conjugacy class of x, just compute every element g − 1xg, and to find the centralizer, just compare gx to …

17 Prove that the order of an element in Sn S n equals the least common multiple of the lengths of the cycles in its cycle decomposition. Proof: Let σ ∈Sn σ ∈ S n.

Jul 22, 2016 · Show that if H H is a subgroup of Sn S n the symmetric group of order n n, then either every member of H H is an even permutation or exactly half of the members are even. I …

Feb 5, 2023 · What's the smallest n n for which Sn S n has an element of order 30? 30? Ask Question Asked 2 years, 11 months ago Modified 2 years, 11 months ago