What groups can G/Z(G) be?
40846
When can a (finite) group be written as the quotient of some other group by its center?
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
43832
Which groups are derived subgroups?
92750
Groups where all elements are order 3
73113
Groups and Symmetries
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
112157
If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator?
124224
How many groups of order $n$ with center {e} exist?
134872
Generators of $\text{GL}_{2}(\mathbb{Z})$ group, good reference book?
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
156909
$\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
73988
Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$
93703
Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$