In mathematics, specifically finite group theory, the uniqueness case is one of the three possibilities for groups of characteristic 2 type given by the trichotomy theorem.

The uniqueness case covers groups G of characteristic 2 type with e(G) ≥ 3 that have an almost strongly p-embedded maximal 2-local subgroup for all primes p whose 2-localp-rank is sufficiently large (usually at least 3). Aschbacher ( 1983a , 1983b ) proved that there are no finite simple groups in the uniqueness case.

References

• Aschbacher, Michael (1983a), "The uniqueness case for finite groups. I", Annals of Mathematics , Second Series, 117 (2): 383–454, doi:10.2307/2007081, ISSN   0003-486X, MR   0690850
• Aschbacher, Michael (1983b), "The uniqueness case for finite groups. II", Annals of Mathematics , Second Series, 117 (3): 455–551, doi:10.2307/2007081, ISSN   0003-486X, JSTOR   2007034, MR   0690850
• Stroth, Gernot (1996), "The uniqueness case", in Arasu, K. T.; Dillon, J. F.; Harada, Koichiro; Sehgal, S.; Solomon., R. (eds.), Groups, difference sets, and the Monster (Columbus, OH, 1993), Ohio State Univ. Math. Res. Inst. Publ., vol. 4, Berlin: de Gruyter, pp. 117–126, ISBN   978-3-11-014791-9, MR   1400413