Mixing
Simple groups and subroup [closed]
$begingroup$
Let $G$ be a group of order $d! leq |G| < infty$ which is simple, that is, every group homomorphism $pi : G to K$ is either injective or $im ; pi = {e}$. Show that $G$ has no subgroup $H$ with $|G|/|H| = d$
abstract-algebra
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
asked Jan 31 at 0:33
Yo gengYo geng
111
$endgroup$
closed as off-topic by max_zorn, user3482749, David Hill, Martin Argerami, metamorphy Jan 31 at 5:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, user3482749, David Hill, Martin Argerami, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $G$ be a group of order $d! leq |G| < infty$ which is simple, that is, every group homomorphism $pi : G to K$ is either injective or $im ; pi = {e}$. Show that $G$ has no subgroup $H$ with $|G|/|H| = d$
abstract-algebra
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
asked Jan 31 at 0:33
Yo gengYo geng
111
$endgroup$
closed as off-topic by max_zorn, user3482749, David Hill, Martin Argerami, metamorphy Jan 31 at 5:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, user3482749, David Hill, Martin Argerami, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
Think about the action of $G$ on the cosets of $H$...
$endgroup$
– Hempelicious
Jan 31 at 1:21
$begingroup$
Thank you @Hempelicious
$endgroup$
– Yo geng
Feb 1 at 15:15
add a comment |
$begingroup$
Let $G$ be a group of order $d! leq |G| < infty$ which is simple, that is, every group homomorphism $pi : G to K$ is either injective or $im ; pi = {e}$. Show that $G$ has no subgroup $H$ with $|G|/|H| = d$
abstract-algebra
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
asked Jan 31 at 0:33
Yo gengYo geng
111
$endgroup$
Let $G$ be a group of order $d! leq |G| < infty$ which is simple, that is, every group homomorphism $pi : G to K$ is either injective or $im ; pi = {e}$. Show that $G$ has no subgroup $H$ with $|G|/|H| = d$
abstract-algebra
abstract-algebra
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
asked Jan 31 at 0:33
Yo gengYo geng
111
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
asked Jan 31 at 0:33
Yo gengYo geng
111
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
edited Jan 31 at 1:00
Robert Lewis
48.6k23167
48.6k23167
asked Jan 31 at 0:33
Yo gengYo geng
111
asked Jan 31 at 0:33
Yo gengYo geng
111
asked Jan 31 at 0:33
Yo gengYo geng
111
111
closed as off-topic by max_zorn, user3482749, David Hill, Martin Argerami, metamorphy Jan 31 at 5:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, user3482749, David Hill, Martin Argerami, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by max_zorn, user3482749, David Hill, Martin Argerami, metamorphy Jan 31 at 5:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, user3482749, David Hill, Martin Argerami, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
Think about the action of $G$ on the cosets of $H$...
$endgroup$
– Hempelicious
Jan 31 at 1:21
$begingroup$
Thank you @Hempelicious
$endgroup$
– Yo geng
Feb 1 at 15:15
add a comment |
1
$begingroup$
Think about the action of $G$ on the cosets of $H$...
$endgroup$
– Hempelicious
Jan 31 at 1:21
$begingroup$
Thank you @Hempelicious
$endgroup$
– Yo geng
Feb 1 at 15:15
1
1
$begingroup$
Think about the action of $G$ on the cosets of $H$...
$endgroup$
– Hempelicious
Jan 31 at 1:21
$begingroup$
Think about the action of $G$ on the cosets of $H$...
$endgroup$
– Hempelicious
Jan 31 at 1:21
$begingroup$
Thank you @Hempelicious
$endgroup$
– Yo geng
Feb 1 at 15:15
$begingroup$
Thank you @Hempelicious
$endgroup$
– Yo geng
Feb 1 at 15:15
add a comment |
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$begingroup$
Think about the action of $G$ on the cosets of $H$...
$endgroup$
– Hempelicious
Jan 31 at 1:21
$begingroup$
Thank you @Hempelicious
$endgroup$
– Yo geng
Feb 1 at 15:15