For which numbers $n$ does every group with order $n$ have a non-trivial center?
124224
How many groups of order $n$ with center {e} exist?
78283
Centralizer of a given element in $S_n$?
158975
Isomorphism of centers of isomorphic groups
89508
Existence of normal subgroups for a group of order $36$
1577
Order of nontrivial elements is 2 implies Abelian group
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
134376
Let $G$ be a nonabelian group. Let $a \in G$ have order $4$ and let $b \in G$ have order $3$. Then the order of the element $ab$ in $G$
74978
How the center of a non-cyclic free Group is trivial?
19720
A normal subgroup intersects the center of the $p$-group nontrivially
56607
gcd and order of elements of group
18881
Number of elements of order $7$ in a group
104509
The center of $A_n$ is trivial for $n \geq 4$
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
2304
What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
42469
Find all groups of order $6$.
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.