Let G be a group of order 2n with n being an odd integer. Prove that G has a normal subgroup of order n.
53409
Show group of order $4n + 2$ has a subgroup of index 2.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
121423
Prove that every element of a finite group has an order
28722
Prove that $H$ is a abelian subgroup of odd order
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
80186
How to show that $K\leq S_4$ is a normal subgroup?
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
138406
If N and every subgroup of N is normal in G then G/N is abelian .
89508
Existence of normal subgroups for a group of order $36$
108250
A group of order $595$ has a normal Sylow 17-subgroup.
102622
K is a subgroup of G. Show that K is not a normal subgroup
138108
If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.
134376
Let $G$ be a nonabelian group. Let $a \in G$ have order $4$ and let $b \in G$ have order $3$. Then the order of the element $ab$ in $G$
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$
92057
Prove that for every odd integer n, there is a group...
133298
Assume $|G|=40$. Show that the subgroup of order $8$ is normal and unique.