The center of a group $G$ is a subgroup of $G$
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
40846
When can a (finite) group be written as the quotient of some other group by its center?
51352
Subgroups of a finite abelian group
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
33728
Basis for Center of Group Ring
7418
The Center of $\operatorname{GL}(n,k)$
98542
Prove that $H$ is a subgroup of an abelian group $G$
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
45028
How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a$ is in center of the group $G$
24181
Showing that $G$ is a group under an alternative operation.
124224
How many groups of order $n$ with center {e} exist?
59041
Centre of $GL_n(\mathbb R)$