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Let J be a finite-dimensional nilpotent algebra over a finite field F_q. Weformulate a procedure for analysing characters of the group 1+J. In particular,we study characters of the group $U_n (q)$ of unipotent triangular $n\times n$matrices over F_q. Using our procedure, we compute the number of irreduciblecharacters of $U_n (q)$ of each degree for n<14. Also, we explain andgeneralise a phenomenon concerning the group $U_{13}(2)$ discovered by Isaacsand Karagueuzian.

Reduction for characters of finite algebra groups