Prove that every non-abelian group of order 6 has a non normal subgroup of order 2.
87696
Use every non-abelian group of order 6 has a non-normal subgroup of order 2 to classify groups of order 6.
28722
Prove that $H$ is a abelian subgroup of odd order
138406
If N and every subgroup of N is normal in G then G/N is abelian .
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
61373
A normal subgroup that is not a characteristic
42469
Find all groups of order $6$.
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
1577
Order of nontrivial elements is 2 implies Abelian group
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
97928
Normal subgroup of a normal subgroup
141125
Group with order $p^2$ must be abelian . How to prove that?
157841
Existence of a non-abelian group of order $p^n$.
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
145254
$G$ be a non-nilpotent and supersoluble finite group.