Addendum to “Construction of (16, 6)-Configurations from a Group of Order 16” by Gonzalez-Dorrego

✍ Scribed by J.H. Keum

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 199 KB
• Volume: 216
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7758

✦ Synopsis

Recently, Gonzalez-Dorrego has given a list of 9 different ways of constructing a nondegenerate (16, 6) configuration from a group of order 16 (up to automorphisms and translations of the group). In this paper, using her algorithm with a minor correction, we obtain 27 such constructions, completing the list. It turns out that the Kummer configuration, which appears geometrically as 16 nodes and 16 tropes of a Jacobian Kummer surface in p3, can be obtained in 24 different ways from 12 different groups. The configuration of type (A) arises in a unique way from the abelian group ~8 x ~2, and the one of type (B) is obtained in two ways from the groups 16F2b and Q8 x ~'2.