Commutative Semifields of Order 35
I. F. Rúa, Elías F. Combarro · Communications in Algebra · 2012
A concrete construction of a commutative semifield of order 35 is introduced. This semifield is proved to be not isotopic to 𝔽35 or Albert's twisted fields of such an order. It is shown that it is equivalent up to the action of the symmetric group S 3 neither to any of those semifields nor to Coulter–Matthews or Ding–Yuan semifields with 35 elements. Also, a complete description of commutative semifields of order 35 is provided, with the help of computational tools. As a consequence, the existence of a completely new semifield is revealed.