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Questions about the branch of algebra that deals with groups.

2 votes
2 answers
340 views

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 …
Tree's user avatar
  • 117
3 votes
1 answer
148 views

Splitting of regular semisimple conjugacy classes in $SL_{n}(q)$

I have the following question: Consider the following two finite groups: $GL_{n}(q)$ and $SL_{n}(q)$. What I am trying to understand is the regular semisimple conjugacy classes of $SL_{n}(q)$. Now, f …
Tree's user avatar
  • 117
3 votes
1 answer
831 views

Regular semisimple elements in $SL(n,q)$

Consider $G=GL(n,q)$. A regular semisimple element of this group, is a matrix, whose characterestic polynomial is square-free and same as minimal polynomial. Results show that the number of such matr …
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  • 117