Show that a 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
70034
Showing that this set of functions is a group.
13631
Showing group with $p^2$ elements is Abelian
63359
Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
71420
Prove that a group is abelian.
8746
Groups of order $pq$ without using Sylow theorems
90584
Show set of affine transformations is a group
151193
Simple subgroup of Symmetric Group
67471
Extending to a disc means fundamental group is trivial
68971
Elementary approach to proving that a group of order 9 is Abelian
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
141379
All groups where underlying set has at most 4 elements
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
13807
Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
115574
Finitely presented group with fewer relations than generators.
101735
A finite $p$-group cannot be simple unless it has order $p$