I Quotienting out by M

1,456
44
If ##N \trianglelefteq H ##, ##N \trianglelefteq G ##, and ##H \le G##, then is it true that ##H/N \le G/N##?

I want to use the result for a proof I am currently doing, but I am not sure it is true.
Is it enough just to note that if ##h_1,h_2\in H##, then ##(h_1N)(h_2^{-1}N) = h_2h_2^{-1}N \in H/N##?
 

fresh_42

Mentor
Insights Author
2018 Award
11,089
7,626

Want to reply to this thread?

"Quotienting out by M" You must log in or register to reply here.

Related Threads for: Quotienting out by M

Replies
7
Views
432
Replies
19
Views
1K
Replies
0
Views
859
  • Posted
Replies
8
Views
3K
  • Posted
Replies
2
Views
969

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top