Let $H$ be a normal p-subgroup of a group $G$. Proof $H$ is contained in $S$ for all $S$ Sylow p-subgroup of G.
118337
Let $S$ be a normal p-subgroup of a finite group $G$. Prove that $S \subseteq P$ for every Sylow p-subgroup $P$ of $G$
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
39469
If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
65037
$H$ is a maximal normal subgroup of $G$ if and only if $G/H$ is simple.
58251
To show every sylow p-subgroup is normal in G
34902
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
70373
Intersection of normal subgroups proof
55178
When there is a unique Sylow p-subgroup it is normal, does this mean that non-unique p-subgroups are not normal?
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
27215
Intersection of the $p$-sylow and $q$-sylow subgroups of group $G$