Can a Finitely Generated Group Contain an Infinitely Generated Subgroup?

  • Thread starter Thread starter tgt
  • Start date Start date
  • Tags Tags
    Groups
tgt
Messages
519
Reaction score
2
Could a finitely generated group contain a subgroup which is infinitely generated? Why?
 
Physics news on Phys.org
What does it mean that a group G is finitely generated? Can you give a definition?
What does a subgroup of G look like?
 
Consider the free group generated by two elements a and b. I think you should be able to show that the subgroup generated by terms of the form bnab-n is not finitely generated.
 
Thread 'Derivation of equations of stress tensor transformation'

Thread 'Derivation of equations of stress tensor transformation'

Hello ! I derived equations of stress tensor 2D transformation. Some details: I have plane ABCD in two cases (see top on the pic) and I know tensor components for case 1 only. Only plane ABCD rotate in two cases (top of the picture) but not coordinate system. Coordinate system rotates only on the bottom of picture. I want to obtain expression that connects tensor for case 1 and tensor for case 2. My attempt: Are these equations correct? Is there more easier expression for stress tensor...
View full post »

Similar threads

I Generators of translations
Replies
0
Views
2K
A What is the generator of the cyclic group (Z,+)?
Replies
7
Views
4K
MHB Proving Finite Groups: A Contradiction in Subgroups - Hello! (Wave)
Replies
12
Views
3K
I What is the importance of p-Sylow subgroups in understanding group structure?
Replies
2
Views
2K
A Difference Between Subgroup & Closed Subgroup of a Group
Replies
14
Views
3K
I Can a group be isomorphic to one of its quotients?
Replies
4
Views
2K
I Differences between left vs right actions in some group theory questions
Replies
1
Views
174
How Is the Abelianization of a Lie Group Defined?
Replies
3
Views
2K
MHB Comparing $gH$ and $Hg$ for Infinite & Finite Groups
Replies
4
Views
3K
MHB Z6: Identity, Order, Inverse, Generator, Abelian/Non-Abelian, Subgroups
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top