Is it true that when $n \geq 5$ there is a surjective homomorphism from the symmetric group $S_n$ to $S_{n-1}$?
108691
Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
131946
Order of an Element Under a Homomorphism
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
83061
Generating the symmetric group $S_n$
136083
Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
121257
Image of Homomorphism of Lie groups
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
35472
Transitive subgroup of symmetric group $S_n$ containing an $(n-1)$-cycle and a transposition
41709
Show that the symmetric group $S_p = $, where $\sigma$ is any transposition and $\tau$ is any p- cycle and p is a prime number.
51334
Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?
50762
If $S_n$ has cyclic subgroups of these orders or not?
44480
Let $\sigma :\{1,2,3,4,5\} \rightarrow \{1,2,3,4,5\}$ be permutations such that $ \sigma^{-1}(j) \leq \sigma(j)~\forall j, 1 \leq j \leq 5$.
137691
What are the self-normalizing subgroups of $S_n$?