Upper bounds on the number of conjugacy classes in unitriangular groups

preprint2015arXivOpen access

We provide a new upper bound on the number of conjugacy classes in the group $U_n(q)$ of unitriangular matrices over a finite field. We also compute a similar upper bound for every group in the lower central series of $U_n(q)$ .

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Upper bounds on the number of conjugacy classes in unitriangular groups

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