Algebra group implies power degree group for field size
From Groupprops
This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., algebra group) must also satisfy the second group property (i.e., power degree group for a prime power)
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Statement
Suppose is a nilpotent associative algebra over a finite field
for a prime power
, and
is the algebra group corresponding to
. Then,
is a q-power degree group: all its degrees of irreducible representations are powers of
.