All Questions
7 questions
2
votes
0
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203
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Can the relation between count of commuting pairs and conjugacy classes for finite groups be generalized to semigroups?
It is well-known that number of pairs of commuting elements in finite group G is equal to number of conjugacy classes multiplied by cardinality of G.
More generally here (MO275769) Qiaochu Yuan ...
- 24.9k
5
votes
1
answer
764
views
Conjugacy classes in $GL_{n}(Z / pZ)$
Let $p$ be a prime number and $G=GL_n ( \mathbb{Z} / p \mathbb{Z}
)$. Consider the set $U$ of upper-triangular matrices of $G$
having entries of $1$ on the diagonal. The cardinality of $U$ is $p^{\...
- 9,501
3
votes
0
answers
147
views
Under what conditions on $A$ and $v$ is the size of the sumset $v \cdot A + A$ over $\mathbb{F}_p$ equal or close to $|A|^2$?
Let $p$ be a prime, let $A$ be a subset of $\mathbb{F}_p$, and let $v \in \mathbb{F}_p \setminus \{0\}$.
Under what conditions is $|v \cdot A + A|$ (that is, $|\{ va + b : a \in A,\ b \in A \}|$) ...
2
votes
0
answers
186
views
Sum of reciprocals in finite fields
Let $p$ be an odd prime number which large enough. I am interested in the study of the sums of reciprocals in the field $\mathbb{F}_p$.
In particular, I have the following question:
which primes $p$ ...
- 4,713
13
votes
2
answers
1k
views
Number of commuting pairs (triples, n-tuples) in GL_n(F_q) (and other groups)?
Question 1 What is the number of pairs of commuting elements in GL_n(F_q) ?
I am aware of many results concerning commuting elements in Mat_n(F_q), but I am interested in GL i.e. non-degenerate ...
- 24.9k
4
votes
1
answer
491
views
What is the permutation group generated by those three given morphisms of the affine space $\mathbb{F}_q^3$?
Let $\mathbb{A}^3 = \mathbb{F}_q^3$. Consider the following three functions $\mathbb{A}^3\to\mathbb{A}^3$:
\begin{eqnarray*}
h: (x, y, z) &\mapsto& (x, y, xy - z) \\
u: (x, y, z) &\mapsto&...
- 22.5k
8
votes
0
answers
304
views
A strong sum-product "for translates" in finite fields
In the course of some recent research, I've sketched out a proof of the following result. My basis question is: is the result interesting?
Proposition There exists an absolute constant $c$ such ...
- 11.2k