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New posts in sylow-theory
Group of order $p^{n}$ has normal subgroups of order $p^{k}$
abstract-algebra
group-theory
finite-groups
sylow-theory
A group of order $120$ cannot be simple
abstract-algebra
group-theory
finite-groups
sylow-theory
Proofs of Sylow theorems
group-theory
reference-request
big-list
sylow-theory
What do Sylow 2-subgroups of finite simple groups look like?
finite-groups
sylow-theory
simple-groups
fusion-systems
2-groups
Problem about solvable groups
group-theory
finite-groups
sylow-theory
solvable-groups
Why is $|H \cdot gP|=1$?
group-theory
proof-explanation
group-actions
sylow-theory
If $|G|=12$ with $|Z(G)|=2$, prove that the group $G$ has only one subgroup of order $3$.
abstract-algebra
group-theory
sylow-theory
Show that a group of order $180$ is not simple.
group-theory
finite-groups
sylow-theory
Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$
abstract-algebra
group-theory
finite-groups
contest-math
sylow-theory
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
abstract-algebra
group-theory
sylow-theory
Sylow 2 subgroups of S4
group-theory
sylow-theory
permutation-cycles
Sylow $p$-subgroup of a direct product is product of Sylow $p$-subgroups of factors
abstract-algebra
group-theory
finite-groups
sylow-theory
Groups of order $56$
abstract-algebra
group-theory
finite-groups
sylow-theory
simple-groups
Maximum number of Sylow subgroups
abstract-algebra
group-theory
finite-groups
sylow-theory
For a group $G$ of order $p^n$, $G\cong H$ for some $H\le\Bbb Z_p\wr\dots\wr\Bbb Z_p$.
group-theory
finite-groups
sylow-theory
p-groups
wreath-product
On Groups of Order 315 with a unique sylow 3-subgroup .
abstract-algebra
group-theory
finite-groups
abelian-groups
sylow-theory
If H is a subgroup of G, then H has no more Sylow subgroups than G
abstract-algebra
group-theory
finite-groups
sylow-theory
Groups of order $pqr$ and their normal subgroups
abstract-algebra
group-theory
sylow-theory
How big must the union of a group's Sylow p-subgroups be?
group-theory
inequality
finite-groups
sylow-theory
A finite $p$-group cannot be simple unless it has order $p$
abstract-algebra
group-theory
finite-groups
sylow-theory
p-groups
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