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Results tagged with conjugacy-classes
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user 28104
4
votes
1
answer
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views
Lower bound on size of largest conjugacy class of centreless perfect group
Problem 20.30 in the Kourovka Notebook asks whether the maximum size
of a conjugacy class of a perfect and centreless finite group $G$ is bounded below
by $|G|^{\frac{1}{2}}$. Clearly, there cannot be …
- 19.6k
16
votes
Conjugacy classes of $\mathrm{SL}_2(\mathbb{Z})$
The conjugacy classes of elements of ${\rm SL}(2,\mathbb{Z})$
with given trace are counted in:
S. Chowla, J. Cowles and M. Cowles:
On the number of conjugacy classes in SL(2,Z).
Journal of Number …
- 19.6k
17
votes
Is there an infinite group with exactly two conjugacy classes?
The answer to the question is yes, even if one
additionally requires the group to be finitely generated.
In this case, the question is Problem 9.10 in the Kourovka Notebook,
and has been answered in: …
- 19.6k