Prove that the symmetric group $S_n$, $n \geq 3$, has trivial center.
11627
Find the center of the symmetry group $S_n$.
117414
How would I prove what elements $S_3$ contains, and what its subgroups are?
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
151193
Simple subgroup of Symmetric Group
29802
Part of simple proof of nontrivial center in p-group
11393
The center of the dihedral group
87823
GAP: how to work with elements of the group ring of the symmetric group $\mathbb{C}[S_k]$?
5089
An element of a group has the same order as its inverse
21568
Maximal order of an element in a symmetric group
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
90764
Prove that the fundamental group of the circle is non-trivial if the fundamental group of a space $X$ is non-trivial
83916
Center of dihedral group
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
14666
What are the non-trivial normal subgroups of $O(3)$?
28576
Galois Groups are isomorphic to subgroups of symmetric groups.
33728
Basis for Center of Group Ring