Show that $(G,*)$ is a group
90584
Show set of affine transformations is a group
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
99346
Prove a result on transitive group actions.
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
60208
Proof of property of abelian group
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
79933
Let $G$ be a group and $c\in G$. Define $*$ on $G$ by: $x*y=xdy$ for all $x,y\in G$, where $d$ is the inverse of $c$. Prove $(G,*)$ is a group.
5599
Proving an inclusion for the derived group
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
65900
Show that a finite group with certain automorphism is abelian
103216
The set $\{g^2 | g \in G\}$ in a group $G$
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
63780
to show characteristic subgroup is normal in G
3462
Proving a set of automorphisms of a group is a group under composition