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New posts in symmetric-groups
What are the self-normalizing subgroups of $S_n$?
abstract-algebra
group-theory
finite-groups
symmetric-groups
normal-subgroups
No group has commutator isomorphic to S_4
finite-groups
symmetric-groups
simple-groups
solvable-groups
What is the smallest $n$ for which the usual "counting sizes of conjugacy classes" proof of simplicity fails for $A_n$?
abstract-algebra
group-theory
finite-groups
symmetric-groups
Show that there is no subgroup of $S_n$ of order $(n-1)!/n$.
abstract-algebra
group-theory
permutations
symmetric-groups
Find a combinatorial proof to 10!=7!6!
combinatorics
group-theory
factorial
symmetric-groups
Algebraic argument for why any $A_5$ in $S_6$ can be extended to an $S_5$ in $S_6$
group-theory
symmetric-groups
platonic-solids
What does it mean when people say that groups are a study of symmetry?
group-theory
symmetric-groups
semigroups
$SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong A_4$
group-theory
symmetric-groups
group-isomorphism
exceptional-isomorphisms
How does showing $\tau(i) = j \implies a\tau a^{-1}(a(i)) = a(j)$ demonstrate that $a\tau a^{-1}$ has the same cycle type as $\tau$?
group-theory
symmetric-groups
Quotient space of $\Bbb C^n$ obtained by action of $S_n$
symmetric-groups
group-actions
Which finite groups have their minimal permutation degree equal to their order?
group-theory
permutations
finite-groups
symmetric-groups
quaternions
Subgroups of $S_n$ of index $n$ are isomorphic to $ S_{n-1}$
group-theory
finite-groups
symmetric-groups
$S_3$ acting on a subgroup -- confirming my computation is correct
group-theory
finite-groups
group-actions
symmetric-groups
$[L:K]=n!\ \Longrightarrow \ f$ is irreducible and $\text{Gal}(L/K)\cong S_n.$
polynomials
field-theory
galois-theory
symmetric-groups
irreducible-polynomials
Why is the conjugacy class of an element in a symmetric group the same as the set of all elements with the same cycle type?
group-theory
symmetric-groups
If $n\ge m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
abstract-algebra
combinatorics
permutations
symmetric-groups
Prove $S_4$ has only 1 subgroup of order 12
group-theory
symmetric-groups
permutations
Elements of $S_n$ can be written as a product of $k$-cycles.
abstract-algebra
group-theory
permutations
symmetric-groups
permutation-cycles
Irreducibility of the standard representation of $S_n$. [duplicate]
representation-theory
permutations
symmetric-groups
How we can find the symmetric group with least $n$ whose subgroup of it is isomorphic to $G$?
group-theory
symmetric-groups
group-isomorphism
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