Why doesn't this presentation embed?

In summary, the conversation discusses the notation <G,t|-> and its meaning as the free group generated by G U {t}. The concept of embedding presentations is also mentioned, with the clarification that embedding means there exists an injective homomorphism. It is also noted that <G,t|-> is not necessarily equal to the free group generated by G U {t}, as the former is the free product of G with {t}.
  • #1
tgt
522
2
How to show <G,t|t^{-1}kt=k, k in K> does not embed into <G,t|->?

Where K is a subgroup of an arbitrary group G.
 
Physics news on Phys.org
  • #2
I admit I don't know much about this stuff, but what exactly does <G,t|-> mean? Is it the free group generated by the set [itex]G \cup \{t\}[/itex]? And how are you defining the embedding of presentations?
 
  • #3
morphism said:
I admit I don't know much about this stuff, but what exactly does <G,t|-> mean? Is it the free group generated by the set [itex]G \cup \{t\}[/itex]? And how are you defining the embedding of presentations?

If G=<X|R> where X is the generating set for G and R are the relations in G then <G,t|-> is <X,t|R>.

Embedding means there exists an injective homomorphism.
 
  • #4
I still don't understand. What is "-", the empty relation? If so then isn't what I asked true: <G,t|-> is the free group generated by [itex]G \cup \{t\}[/itex]?
 
  • #5
morphism said:
I still don't understand. What is "-", the empty relation? If so then isn't what I asked true: <G,t|-> is the free group generated by [itex]G \cup \{t\}[/itex]?

I never said you were wrong. I like to only use the term free group for groups generated from a basis only. What I said in the previous post has no mistakes either.
 
  • #6
Correction, you were actually wrong. The free group generated by G U {t} will be greater. i.e take G={a,b} with the relations a=1, bb=1. Those relations will hold in <G,t|-> but not in the free group. In fact <G,t|-> is the free product of G with {t}.
 

1. Why isn't the presentation embedding properly?

There could be several reasons why the presentation is not embedding properly. It could be due to compatibility issues with the file format, internet connectivity issues, or incorrect embedding code.

2. How can I fix the problem with the presentation not embedding?

To fix the issue, try using a different file format for the presentation, ensure that you have a stable internet connection, and double check the embedding code for any errors.

3. Is there a specific browser that I should use for the presentation to embed?

No, presentations should be able to embed on all major browsers. However, if you are using an older browser version, there may be compatibility issues.

4. Can I embed a presentation from a different platform?

Yes, as long as the platform supports embedding and provides the necessary code, you should be able to embed the presentation on your website or presentation.

5. Why is the presentation not showing up after I embed it?

This could be due to a slow internet connection or incorrect embedding code. Try refreshing the page or checking the code for any errors.

Similar threads

  • Linear and Abstract Algebra
Replies
1
Views
730
  • Linear and Abstract Algebra
Replies
1
Views
652
  • Linear and Abstract Algebra
Replies
2
Views
1K
  • Linear and Abstract Algebra
Replies
11
Views
1K
  • Linear and Abstract Algebra
Replies
5
Views
1K
  • Linear and Abstract Algebra
Replies
8
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
690
  • Linear and Abstract Algebra
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
16
Views
334
  • Linear and Abstract Algebra
Replies
1
Views
793
Back
Top