Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
13059
If a group is the union of two subgroups, is one subgroup the group itself?
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
132342
Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
66510
A group is abelian if and only if the center of the group is all the group
70373
Intersection of normal subgroups proof
122271
A subset of a transitive set is transitive
54195
Do groups of prime order have one subgroup?
43068
Let A and B be sets. Show that A is a subset of B if and only if for any set C, one has A union C is a subset of B union C.
114431
Monoids and Subgroups
122821
Is the following proof valid? About the closure of a subgroup, of a topological group, being again a subgroup
98474
Show the existence of a certain subgroup of F2
124732
Finding a nonempty subset that is not a subgroup
71232
if $A$ is Abelian group , $B$ is subgroup of $A$ , Is $B \times A/B \cong A$?
157330
Showing the image of a subgroup is a subgroup.
103002
Group equals union of two subgroups
74970
Subsubgroups are subgroups of subgroups / Multiplicative Property of the Index