Dade's Conjecture for the Simple O'Nan Group
✍ Scribed by Katsuhiro Uno; Satoshi Yoshiara
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 287 KB
- Volume
- 249
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let G be a finite group, p a rational prime number, and ,ދ R, F a ''sufficiently large'' p-modular system. This includes the requirement that R is a complete discrete valuation ring of characteristic 0, with field of Ž . fractions ,ދ such that F s RrJ R is algebraically closed of characteristic
For such a p-chain C we denote m j=0 N G U j by N G C , and by C we denote the length m of C. Moreover, for a given p-block B of G and a non-negative integer d, let Irr N G C B d denote the set of irreducible characters χ of N G C , such that χ belongs to a block of N G C inducing B and such that p
We verify the inductive form of Dade's conjecture for the finite simple groups 2 G 2 3 2m+1 , where m is a positive integer, for the prime p = 3. Together with work by J. An (1994, Indian J. Math. 36, 7-27) this completes the verification of the conjecture for this series of groups.
We show that, for the O'Nan sporadic simple group, there is no Rwpri and (IP) 2 geometry of rank 6 with a maximal parabolic subgroup isomorphic to M 11 and that there is no Rwpri and (IP) 2 geometry of rank 5 with a maximal parabolic subgroup isomorphic to J 1 . This last result permits us to show t
The McKay conjecture states that the number of irreducible complex characters of a group G that have degree prime to p is equal to the same number for the Sylow p-normalizer in G. We verify this conjecture for the 26 sporadic simple groups.