Show that a finite group of even order that has a cyclic Sylow $2-$ subgroup is not simple.
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
35401
Examples of finite groups that are not a semidirect product
2731
Groups of even order have an element whose order is 2.
107716
Show that $G$ is cyclic
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
28210
A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
28181
Sylow subgroups of $S_3$ and $S_4$
114187
In a finite cyclic group, the generator has the order of the group
67554
In a group, the number of non-self-inverse elements is even
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
51196
A group of order $p^2q^2$ is never simple
152954
Extensions of finite cyclic groups
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
87534
Finitely generated group which is not finitely presented
61550
Existence of elements of order $p^k$ in a finite group
61394
The product of finitely many cyclic groups is cyclic
76504
Non-trivial cyclic group with unique generator