Sylow Theorems/Examples
Jump to navigation
Jump to search
Examples of Use of Sylow Theorems
Sylow $2$-Subgroups in Group of Order $12$
In a group of order $12$, there are either $1$ or $3$ Sylow $2$-subgroups.
Sylow $3$-Subgroups in Group of Order $12$
In a group of order $12$, there are either $1$ or $4$ Sylow $3$-subgroups.
Sylow $7$-Subgroups in Group of Order $28$
In a group of order $28$, there exists exactly $1$ Sylow $7$-subgroup.
This Sylow $7$-subgroup is normal in $G$.
Sylow $2$-Subgroups in Group of Order $32$
The Sylow Theorems tell us nothing about the Sylow $2$-subgroups in a group of order $32$.
Sylow $2$-Subgroups in Group of Order $48$
In a group of order $48$, there are either $1$ or $3$ Sylow $2$-subgroups.