Show that for each integer $n ≥ 2$, $F_n$ is a finite index subgroup of $F_2$, where $F_n$ is the free group on $n$ generators.
57309
Show that the free group on $n$ generators is a finite index subgroup of $F_2$
12667
How many subgroups of order $n$ does $D_n$ have?
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
115973
Computing the number of nonisomorphic finite abelian groups of order $n$
58076
Subgroup generated by a set
131516
Subgroup generated by n-th powers of elements
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
154398
Show that H is a subgroup of G
75568
Subgroup of index $2$ is Normal
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
54082
Group with exactly two subgroups of index 2
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
108691
Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
149578
Subgroups of $(\mathbb Z_n,+)$
104855
Prove that $N \subset Z(G)$