Show there is no non-abelian group of order 9
68971
Elementary approach to proving that a group of order 9 is Abelian
118022
Show that a group of order $180$ is not simple.
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
90329
Prove there is no simple group of order $729$
129937
How to prove that $A_5$ has no subgroup of order 30?
1577
Order of nontrivial elements is 2 implies Abelian group
65900
Show that a finite group with certain automorphism is abelian
16259
How many non isomorphic groups of order 30 are there?
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
89508
Existence of normal subgroups for a group of order $36$
29538
Does a non-abelian semigroup without identity exist?
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
76943
Existence of subgroup of order six in $A_4$
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
152630
showing that a group of order 45 is abelian
63798
How can you show there are only 2 nonabelian groups of order 8?