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Sean Lawton
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Is Sizethe size of a conjugacy classesclass in Finitea finite classical groups polynomialsgroup a polynomial?

Suppose $G$ is a classical matrix group over a finite field.If $C$ is any conjugacy class of $G$ , then is $|C|$ is a polynomial inorder $q$.

If $C$ is a conjugacy class in $G$ , is $|C|$ a polynomial in $q$?

This question is encouraged fromsupported by the fact that whenever I have calculated all conjugacy classes and itstheir sizes for very small groups, for (for example, $GL_{2}(\mathbb{F}_{q})$, $GL_{3}(\mathbb{F}_{q})$, $SL_{2}(\mathbb{F}_{q})$, $SL_{3}(\mathbb{F}_{q})$, it does) the sizes of conjugacy classes turn out to be polynomialspolynomial in $q$. 

So, is it true indoes this property hold for all finite classical group, or at least even in the case of $GL_n$ or $SL_n$?

Thanks!

Is Size of conjugacy classes in Finite classical groups polynomials?

Suppose $G$ is a classical matrix group over a finite field.If $C$ is any conjugacy class of $G$ , then is $|C|$ is a polynomial in $q$. This question is encouraged from the fact whenever I have calculated all conjugacy classes and its sizes for very small groups, for example, $GL_{2}(\mathbb{F}_{q})$, $GL_{3}(\mathbb{F}_{q})$, $SL_{2}(\mathbb{F}_{q})$, $SL_{3}(\mathbb{F}_{q})$, it does turn out to be polynomials in $q$. So, is it true in all finite classical group or at least even in the case of $GL_n$ or $SL_n$?

Thanks!

Is the size of a conjugacy class in a finite classical group a polynomial?

Suppose $G$ is a classical matrix group over a finite field of order $q$.

If $C$ is a conjugacy class in $G$ , is $|C|$ a polynomial in $q$?

This question is supported by the fact that whenever I have calculated all conjugacy classes and their sizes for very small groups (for example, $GL_{2}(\mathbb{F}_{q})$, $GL_{3}(\mathbb{F}_{q})$, $SL_{2}(\mathbb{F}_{q})$, $SL_{3}(\mathbb{F}_{q})$) the sizes of conjugacy classes turn out to be polynomial in $q$. 

So, does this property hold for all finite classical group, or at least the case of $GL_n$ or $SL_n$?

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Is Size of conjugacy classes in Finite classical groups polynomials?

Suppose $G$ is a classical matrix group over a finite field.If $C$ is any conjugacy class of $G$ , then is $|C|$ is a polynomial in $q$. This question is encouraged from the fact whenever I have calculated all conjugacy classes and its sizes for very small groups, for example, $GL_{2}(\mathbb{F}_{q})$, $GL_{3}(\mathbb{F}_{q})$, $SL_{2}(\mathbb{F}_{q})$, $SL_{3}(\mathbb{F}_{q})$, it does turn out to be polynomials in $q$. So, is it true in all finite classical group or at least even in the case of $GL_n$ or $SL_n$?

Thanks!