Algebra groups, which generalize the group of unimodular, upper-triangular matrices over a finite field, are studied. The primary focus is on supercharacters, a sort of replacement for irreducible characters. Kirillov functions and a conjecture of Eggert are also discussed.;The main results follow. The number of superdegrees bounds for the nilpotence class of the underlying algebra; likewise for superclass sizes. Every set of p-powers that contains 1 is a set of superdegrees and a set of superclass sizes. The logarithm modification of Kirillov functions cannot improve supercharacters. Every constituent of a Kirillov function is a constituent of the corresponding supercharacter, and this relationship is stronger for linear constituents.
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