Prove that there is no simple group of order $216=2^{3}\cdot 3^{3}$.
15706
"Every Group of order $216$ contains a normal subgroup of order $27$ or $9$
131306
Prove that a group of order $2^5 \cdot 7^5$ is not simple
99309
Groups of order $n^2$ that have no subgroup of order $n$
46986
No group of order 400 is simple
34972
order of non abelian group can't be what?
121142
Take $G$ to be a group of order $600$. Prove that for any element a in $G$ there exist a $b$ in $G$ such that $a = b^7$
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
129120
Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
80849
There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
151029
The number of non normal subgroups of a group cannot be $1$?
148904
Groups of order $p^3$
96764
No simple group of order 2016
113840
Does converse of Lagrange's theorem hold for a group of order 21?
126893
A group of order 2p (p prime) and other conditions - prove abelian.
150760
Are there any distinct finite simple groups with the same order?
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$