Show that a group can not be expressed as union of two of its proper subgroups
13059
If a group is the union of two subgroups, is one subgroup the group itself?
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
70373
Intersection of normal subgroups proof
51196
A group of order $p^2q^2$ is never simple
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
61373
A normal subgroup that is not a characteristic
154398
Show that H is a subgroup of G
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
34552
Proper subgroups of non-cyclic p-group cannot be all cyclic?
91021
Torsion elements of a group aren't necessarily a subgroup
99309
Groups of order $n^2$ that have no subgroup of order $n$
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
113413
How do I show that two groups are not isomorphic?
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
90081
problems in group theory
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$