Newbetuts

Let $a$ be a p-cycle in $S_p$, and let $b$ be a transposition in $S_p$. Show $S_p$ is generated by $a$ and $b$.

What is symmetric about the symmetric group? [duplicate]

Generalization of index 2 subgroups are normal

Orders of a symmetric group

$\operatorname{Aut}(S_4)$ is isomorphic to $S_4$

Normal subgroups of $S_n$ for $n\geq 5$.

Group presentation of $A_5$ with two generators

Show that any abelian transitive subgroup of $S_n$ has order $n$

Assume $H\le S_n$ contains an element of order $n$ and a transposition. Given that $n$ is prime, does $H=S_n$? [duplicate]

Which vertex-transitive planar graphs represent non-self-intersecting polyhedra?

Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative

How many distinct subgroups does the symmetric group $S_3$ have?

Functional Equations, Linear Symmetry, Group Theory

What does an outer automorphism look like?

How to show that $K\leq S_4$ is a normal subgroup?

How powerful is Cayley's theorem?

Finding the left and right cosets of $H=\{(1),(12),(34),(12) \circ(34)\}$ in $S_4$

New posts in symmetric-groups

Logic for decomposing a permutation into different products composed of transpositions

Find the derived subgroup of $A_4$

Generating the symmetric group $S_n$

Let $a$ be a p-cycle in $S_p$, and let $b$ be a transposition in $S_p$. Show $S_p$ is generated by $a$ and $b$.

What is symmetric about the symmetric group? [duplicate]

Generalization of index 2 subgroups are normal

Orders of a symmetric group

$\operatorname{Aut}(S_4)$ is isomorphic to $S_4$

Normal subgroups of $S_n$ for $n\geq 5$.

Group presentation of $A_5$ with two generators

Show that any abelian transitive subgroup of $S_n$ has order $n$

Assume $H\le S_n$ contains an element of order $n$ and a transposition. Given that $n$ is prime, does $H=S_n$? [duplicate]

Which vertex-transitive planar graphs represent non-self-intersecting polyhedra?

Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative

How many distinct subgroups does the symmetric group $S_3$ have?

Functional Equations, Linear Symmetry, Group Theory

What does an outer automorphism look like?

How to show that $K\leq S_4$ is a normal subgroup?

How powerful is Cayley's theorem?

Finding the left and right cosets of $H=\{(1),(12),(34),(12) \circ(34)\}$ in $S_4$