The intersection of maximal subgroups of abelian group is not trivial.
9612
Frattini subgroup $Φ ( G )$ is not trivial
47731
Intersection of all $p$-Sylow subgroups is normal
23941
Normal Subgroups that Intersect Trivially
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
19720
A normal subgroup intersects the center of the $p$-group nontrivially
10602
Monotone Union of subgroups being subgroup
71035
Non abelian subgroup of a abelian group.
57227
Maximal normal $\pi$-subgroups and torsion subgroups
151287
Isomorphic abelian groups which are not isomorphic R-modules
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
91021
Torsion elements of a group aren't necessarily a subgroup
3907
Abelian quotient group
156941
Subgroups of $\mathbb{Z}$
90332
Prove that that $U(n)$ is an abelian group.
24181
Showing that $G$ is a group under an alternative operation.
27215
Intersection of the $p$-sylow and $q$-sylow subgroups of group $G$