If $G$ is an infinite group, and $A,B$ subgroups of finite index in $ G$, then $A \cap B$ has finite index in $G$
46121
Does the intersection of two finite index subgroups have finite index?
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
47539
Find an abelian infinite group such that every proper subgroup is finite
7121
If $G$ is a finite group and $|G| < |A| + |B|$, then $G=AB$.
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
10816
Infinitely generated subgroup of a finitely one (weird)
126426
Does every infinite finitely generated group contains an element of infinite period?
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
98542
Prove that $H$ is a subgroup of an abelian group $G$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
153921
Infinite nilpotent group, any normal subgroup intersects the center nontrivially
87534
Finitely generated group which is not finitely presented
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
156941
Subgroups of $\mathbb{Z}$