Abelian Group Criteria and counterexample
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
140962
Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
23533
All subgroups normal $\implies$ abelian group
122335
Abelian $p$-group with unique subgroup of index $p$
48393
Abelian groups of order n.
90081
problems in group theory
152630
showing that a group of order 45 is abelian
66806
A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
11113
Group With an Endomorphism That is "Almost" Abelian is Abelian.
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
35188
Counterexample: $G \times K \cong H \times K \implies G \cong H$
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
68971
Elementary approach to proving that a group of order 9 is Abelian
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
3838
If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian?
20658
Difficulty in finding a counterexample
5741
Direct product of abelian groups