Group corresponding to odd-order presemifield that is not isotopic to a commutative presemifield has exactly two abelian normal subgroups of maximum order

History
This result was proved in a paper by Jonah and Konvisser.

Statement
Suppose $$F$$ is a presemifield of odd order (and hence, a finite algebra over a prime field for odd prime $$p$$) that is not isotopic to a commutative presemifield. Let $$G$$ be the corresponding group. Then, $$G$$ has two abelian normal subgroups of maximum order, namely $$p^{2k}$$, where $$p^k$$ is the size of $$F$$. Further, these are also the only two elementary abelian normal subgroups of order $$p^{2k}$$.