Finite semifields with 7⁴ elements

Abstract

In this paper, a highly demanding computer-assisted classification of four-dimensional finite semifields over the field 𝔽₇ is provided. The techniques considered to overcome the difficulties in the management of the large data processed are explained.

Keywords:

• finite semifield
• finite division ring
• computational methods
• classification
• projective planes

2010 AMS Subject Classifications:

• 12K10
• 17D99
• 17-04
• 17-08
• 51A35

Acknowledgements

The authors thank the Centro de Supercomputación y Visualización de Madrid (CeSViMa) and the Spanish Supercomputing Network for providing the computer resources, technical expertise and assistance. They also thank the University of Oviedo SCTs (Servicios Científico Técnicos) for the use of their ‘Cluster de Modelización’. E.F. Combarro and J. Ranilla are partially supported by MICINN-TIN2010-14971, and I.F. Rúa is partially supported by MTM2010-18370-C04-01 and IB08-147.