Fdtxjr

Why doesn't H₄O²⁺ exist?

Western buddy movie with a supernatural twist where a woman turns into an eagle at the end

Is it possible to download Internet Explorer on my Mac running OS X El Capitan?

What reasons are there for a Capitalist to oppose a 100% inheritance tax?

In a Spin are Both Wings Stalled?

How can I prevent hyper evolved versions of regular creatures from wiping out their cousins?

Brothers & sisters

Anagram holiday

Withdrawals from HSA

Arrow those variables!

What's the difference between 'rename' and 'mv'?

90's TV series where a boy goes to another dimension through portal near power lines

Will google still index a page if I use a $_SESSION variable?

Can one be a co-translator of a book, if he does not know the language that the book is translated into?

Etiquette around loan refinance - decision is going to cost first broker a lot of money

Why is Collection not simply treated as Collection<?>

Can I ask the recruiters in my resume to put the reason why I am rejected?

How do conventional missiles fly?

SSH "lag" in LAN on some machines, mixed distros

Can I make "comment-region" comment empty lines?

Python: return float 1.0 as int 1 but float 1.5 as float 1.5

Reserved de-dupe rules

Assassin's bullet with mercury

Blender 2.8 I can't see vertices, edges or faces in edit mode

How many elements in the cyclic group $C_54$ have order $6$? How many have order $8$?

If a cyclic group has an element of infinite order, how many elements of finite order does it have?Abelian group with cyclic subgroup and cyclic quotient is generated by two elementsHow to find a generator of a cyclic group?Why is the set of integers with the operation of addition considered a cyclic group?A prime order group must be cyclicCan $S_n$ be a cyclic group?$(G:H) < infty$ where $G$ is an infinite cyclic groupHow is “integers mod n under addition” a cyclic group?Subgroup of a Dihedral group is Cyclic proofGroup theory problem - the order of elements

-1

$begingroup$

I'm new to the algebra game and I'm learning about group theory at Uni. I understand a cyclic group is a group that can be generated by a single element, but I'm not sure how I would answer the above question.

abstract-algebra group-theory cyclic-groups

share|cite|improve this question

edited Mar 21 at 12:37

Alan Muniz

2,61311030

asked Mar 21 at 12:16

rishi547rishi547

1

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Have you come across Lagrange's theorem? This will let you answer one of the two questions very quickly.
  $endgroup$
  – Arthur
  Mar 21 at 12:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Arthur yep the one which states ..every subgroup H of G divides the order of G, thank you for the help.
  $endgroup$
  – rishi547
  Mar 21 at 12:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @DietrichBurde Ive looked mate, but most of it goes right over my head, thanks for the help though.
  $endgroup$
  – rishi547
  Mar 21 at 12:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Hi Rishi, if an element has order $8$, then the group generated by that element must have order $8$ and be a subgroup of $C_54$, right? Now, by Lagrange's theorem which you correctly stated, $8$ should be a multiple of $54$. Is this true? What can you conclude?
  $endgroup$
  – астон вілла олоф мэллбэрг
  Mar 21 at 12:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  And for $n=6$, the subgroup generated by such an element is isomorphic to $C_6$, and this happens. Then there are $phi(6)=2$ generators.
  $endgroup$
  – Dietrich Burde
  Mar 21 at 14:41
  

  
  
  
  

 | 
show 2 more comments

-1

$begingroup$

I'm new to the algebra game and I'm learning about group theory at Uni. I understand a cyclic group is a group that can be generated by a single element, but I'm not sure how I would answer the above question.

abstract-algebra group-theory cyclic-groups

share|cite|improve this question

edited Mar 21 at 12:37

Alan Muniz

2,61311030

asked Mar 21 at 12:16

rishi547rishi547

1

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Have you come across Lagrange's theorem? This will let you answer one of the two questions very quickly.
  $endgroup$
  – Arthur
  Mar 21 at 12:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Arthur yep the one which states ..every subgroup H of G divides the order of G, thank you for the help.
  $endgroup$
  – rishi547
  Mar 21 at 12:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @DietrichBurde Ive looked mate, but most of it goes right over my head, thanks for the help though.
  $endgroup$
  – rishi547
  Mar 21 at 12:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Hi Rishi, if an element has order $8$, then the group generated by that element must have order $8$ and be a subgroup of $C_54$, right? Now, by Lagrange's theorem which you correctly stated, $8$ should be a multiple of $54$. Is this true? What can you conclude?
  $endgroup$
  – астон вілла олоф мэллбэрг
  Mar 21 at 12:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  And for $n=6$, the subgroup generated by such an element is isomorphic to $C_6$, and this happens. Then there are $phi(6)=2$ generators.
  $endgroup$
  – Dietrich Burde
  Mar 21 at 14:41
  

  
  
  
  

 | 
show 2 more comments

$begingroup$

I'm new to the algebra game and I'm learning about group theory at Uni. I understand a cyclic group is a group that can be generated by a single element, but I'm not sure how I would answer the above question.

abstract-algebra group-theory cyclic-groups

share|cite|improve this question

edited Mar 21 at 12:37

Alan Muniz

2,61311030

asked Mar 21 at 12:16

rishi547rishi547

1

$endgroup$

share|cite|improve this question

edited Mar 21 at 12:37

Alan Muniz

2,61311030

asked Mar 21 at 12:16

rishi547rishi547

1

share|cite|improve this question

edited Mar 21 at 12:37

Alan Muniz

2,61311030

asked Mar 21 at 12:16

rishi547rishi547

1

edited Mar 21 at 12:37

Alan Muniz

2,61311030

edited Mar 21 at 12:37

Alan Muniz

2,61311030

asked Mar 21 at 12:16

rishi547rishi547

1

asked Mar 21 at 12:16

rishi547rishi547

1