Some non-split extensions of the orthogonal group Ω(7,3)

JOURNAL OF ALGEBRA

卷:224

Article

Kitazume, M

关键词: 3-transition groups;    orthogonal groups;    Moufang loops;    trilinear forms;    Conway-Norton algebras;   

DOI  :  10.1006/jabr.1999.8084

来源: Elsevier

【 摘 要 】

We will give an explicit construction of the non-split extension 3(7) . Ohm(7, 3) : 2, which is a maximal subgroup of Fischer's largest 3-transposition group F-24. In the proof of non-splitness, we use some Moufang loop of order 81. By using this loop, we can also construct another non-split extension 3 . Ohm(7, 3) : 2. (C) 2000 academic Press.

【 授权许可】

Free