Show that the group is trivial.
23517
Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
59898
Elementary manipulation with elements of group
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
139218
Is this group solvable?
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
101064
Showing the triviality of homomorphisms
66464
Faithful group actions for singleton group or for empty set
25421
Simple or not simple Groups
66510
A group is abelian if and only if the center of the group is all the group
63253
Computing easy direct limit of groups
133664
When the automorphism group is trivial......
80381
Groups with "few" subgroups
39976
If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
64527
Show that an operation of elements in a finite group contains each element exactly once
98474
Show the existence of a certain subgroup of F2
151193
Simple subgroup of Symmetric Group
130792
Commutator of a group