Summary Report of Previous Project P11486-TEC

As the main practical result of the work on the FWF research project P11486-TEC, a library of functions for working with nearrings has been developed and implemented. The first version of this package called SONATA (System of Nearrings and their Applications) was released on October 1, 1997. In July, a pre-release version of SONATA was presented to the scientific community at the Conference on Nearrings and Nearfields at Stellenbosch, South Africa. The audience was impressed and eagerly looking forward to the final release. We now have a tool that

1. contains a large library of nearrings;
2. can perform all standard constructions for nearrings, N-groups, and their ideals;
3. finds transformation representations of nearrings;
4. helps in analyzing the structure of a big class of nearrings, for example it computes the ideal lattice together with the commutator structure on it.
5. very efficiently deals with big d.g. nearrings, in particular nearrings of type , , and . For example, the nearring has order , which can be computed within five minutes.
6. computes nearring-generated designs and codes for specific parameters;
7. can pretty-print all available information on a given nearring;

All algorithms have been implemented on top of a state-of-the-art package for group theory (GAP) in order to take advantage of the algorithms already available therein.

In addition, this package has been used to solve various theoretical problems and to find errors in the literature as well as to develop various new and error-free (i.e., computer generated) tables.

• GAP data structures
• Library of Nearrings
• Structural Operations
• Documenting Nearrings
• D.G. Nearrings
• Transformation Nearrings
• N-groups
• Semigroups
• Designs
• Codes
• Theoretical investigations
  • Affine complete groups
  • Centralizer nearrings of type
  • Existence of nearrings with identity
  • Polynomial functions on groups of nilpotency class 2
• Errors in the literature
• Release of SONATA
• Official Talks of project members and cooperating staff:
• Publications
• Organization