Show that groups of order $2^2cdot 5^3cdot7^9$ are not simple
$begingroup$
Show that groups of order $2^2cdot 5^3cdot7^9$ are not simple.
I know that in order to be simple, a group who's normal subgroups are the trivial group and the group itself. I also know that $2^2cdot 5^3cdot7^9 = 20176803500$.
I am unsure how to finish this proof
abstract-algebra
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
asked Dec 13 '18 at 22:17
HowardHoward
61
$endgroup$
add a comment |
$begingroup$
Show that groups of order $2^2cdot 5^3cdot7^9$ are not simple.
I know that in order to be simple, a group who's normal subgroups are the trivial group and the group itself. I also know that $2^2cdot 5^3cdot7^9 = 20176803500$.
I am unsure how to finish this proof
abstract-algebra
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
asked Dec 13 '18 at 22:17
HowardHoward
61
$endgroup$
$begingroup$
Use Sylow theorems en.wikipedia.org/wiki/Sylow_theorems
$endgroup$
– Martín Vacas Vignolo
Dec 13 '18 at 22:21
add a comment |
$begingroup$
Show that groups of order $2^2cdot 5^3cdot7^9$ are not simple.
I know that in order to be simple, a group who's normal subgroups are the trivial group and the group itself. I also know that $2^2cdot 5^3cdot7^9 = 20176803500$.
I am unsure how to finish this proof
abstract-algebra
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
asked Dec 13 '18 at 22:17
HowardHoward
61
$endgroup$
Show that groups of order $2^2cdot 5^3cdot7^9$ are not simple.
I know that in order to be simple, a group who's normal subgroups are the trivial group and the group itself. I also know that $2^2cdot 5^3cdot7^9 = 20176803500$.
I am unsure how to finish this proof
abstract-algebra
abstract-algebra
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
asked Dec 13 '18 at 22:17
HowardHoward
61
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
asked Dec 13 '18 at 22:17
HowardHoward
61
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
edited Dec 13 '18 at 22:26
Tianlalu
3,28521238
3,28521238
asked Dec 13 '18 at 22:17
HowardHoward
61
asked Dec 13 '18 at 22:17
HowardHoward
61
asked Dec 13 '18 at 22:17
HowardHoward
61
61
$begingroup$
Use Sylow theorems en.wikipedia.org/wiki/Sylow_theorems
$endgroup$
– Martín Vacas Vignolo
Dec 13 '18 at 22:21
add a comment |
$begingroup$
Use Sylow theorems en.wikipedia.org/wiki/Sylow_theorems
$endgroup$
– Martín Vacas Vignolo
Dec 13 '18 at 22:21
$begingroup$
Use Sylow theorems en.wikipedia.org/wiki/Sylow_theorems
$endgroup$
– Martín Vacas Vignolo
Dec 13 '18 at 22:21
$begingroup$
Use Sylow theorems en.wikipedia.org/wiki/Sylow_theorems
$endgroup$
– Martín Vacas Vignolo
Dec 13 '18 at 22:21
add a comment |
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$begingroup$
Use Sylow theorems en.wikipedia.org/wiki/Sylow_theorems
$endgroup$
– Martín Vacas Vignolo
Dec 13 '18 at 22:21