Newbetuts

Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.

How many homomorphisms are there of $\mathbb{Z}/{3\mathbb{Z}} $ into $S_3$?

Symmetric groups on sets with the same number of elements are isomorphic

Is there a good overview of conjugacy classes?

How many elements of order $k$ are in $S_n$?

elliptic functions on the 17 wallpaper groups

Are reflections in higher dimensions commutative?

Describe the structure of the Sylow $2$-subgroups of the symmetric group of degree $22$

Determine order of $\langle(12345),(2354)\rangle$.

Enumerating all subgroups of the symmetric group

Can someone explain Cayley's Theorem step by step?

$(12)$ and $(123\dots n)$ are generators of $S_n$

Is the continuous part of the symmetry group of a compact subset $\mathbb{R}^3$ isomorphic to $SO(k)$?

Normal subgroups of $S_4$

Splitting of conjugacy class in alternating group

New posts in symmetric-groups

Rotman's exercise 2.8 "$S_n$ cannot be imbedded in $A_{n+1}$"

Probability that two randomly chosen permutations will generate $S_n$.

Embedding $S_n$ into $A_{n+2}$

Can a figure be divided into 2 and 3 but not 6 equal parts?

The alternating group is a normal subgroup of the symmetric group

Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.

How many homomorphisms are there of $\mathbb{Z}/{3\mathbb{Z}} $ into $S_3$?

Symmetric groups on sets with the same number of elements are isomorphic

Is there a good overview of conjugacy classes?

How many elements of order $k$ are in $S_n$?

elliptic functions on the 17 wallpaper groups

Are reflections in higher dimensions commutative?

Describe the structure of the Sylow $2$-subgroups of the symmetric group of degree $22$

Determine order of $\langle(12345),(2354)\rangle$.

Enumerating all subgroups of the symmetric group

Can someone explain Cayley's Theorem step by step?

$(12)$ and $(123\dots n)$ are generators of $S_n$

Is the continuous part of the symmetry group of a compact subset $\mathbb{R}^3$ isomorphic to $SO(k)$?

Normal subgroups of $S_4$

Splitting of conjugacy class in alternating group