The group $G$ has order 56. Show that it contains normal Sylow p-subgroup.
141188
Groups of order $56$
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$
51747
Showing that the intersection of all subgroups of order $n$ is normal
111886
Let $(G,•)$ be a group in which $(a•b)^3 = a^3•b^3$. Prove that $H=\{x^3 : x \in G\}$ is a normal subgroup of $G$.
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
46940
On Groups of Order 315 with a unique sylow 3-subgroup .
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
11957
G is the product of its Sylow subgroups
148904
Groups of order $p^3$
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
59007
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
89508
Existence of normal subgroups for a group of order $36$
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$