Conjugacy Class Problem

  • Thread starter playa007
  • Start date
  • #1
29
0

Homework Statement


If a group has order 20 has 4 conjugacy classes, it must have a trivial centre. True or False?


Homework Equations


The Class Equation

The Attempt at a Solution


I believed the answer to be false with this following counterexample:
20 = lZ(G)l + (20/4 + 20/4 + 20/5 + 20/5) => order of Z(G) = 2 => the centre is non-trivial.
where 5, 5, 4, 4 is the size of the 4 conjugate classes respectively

Any feedback on my reasoning and any flaws are very much appreciated
 

Answers and Replies

  • #2
morphism
Science Advisor
Homework Helper
2,015
4
You haven't demonstrated that such a group exists.
 

Related Threads on Conjugacy Class Problem

  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
0
Views
871
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
13K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
366
Replies
4
Views
3K
Replies
15
Views
2K
Top