A formation is a class 3 of groups which is closed under homomorphic images and is such that each group G has a unique smallest normal subgroup H with factor group in 5. This uniquely determined normal subgroup of G is called the 8-residual subgroup of G and will be denoted here by G,. The formatio
On the Lattice of F-Dnormal Subgroups in Finite Soluble Groups
✍ Scribed by M. Arroyo-Jordá; M.D. Pérez-Ramos
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 154 KB
- Volume
- 242
- Category
- Article
- ISSN
- 0021-8693
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The authors investigate the structure of locally soluble-by-finite groups that satisfy the weak minimal condition on non-nilpotent subgroups. They show, among other things, that every such group is minimax or locally nilpotent.
Let p be a prime number and K be an algebraically closed field of characteristic p. Let G be a finite group and B be a (p-) block of G. We denote by l B the number of isomorphism classes of irreducible KG-modules in B. Let D be a defect group of B and let B 0 be the Brauer correspondent of B, that i
In this paper, a formula is given for the Mo bius number +(1, S n ) of the subgroup lattice of the symmetric group S n . This formula involves the Mo bius numbers of certain transitive subgroups of S n . When n has at most two (not necessarily distinct) prime factors or n is a power of two, this for
## 2 1 2 1 2 4 2 Ž . gam, or a F 2 -amalgam. ## 4 Let G be a nonabelian simple group satisfying the assumption of the Ž . Main Theorem. Then G satisfies the assumption of Theorem 2. If 1 or Ž . 2 occurs in Theorem 2, we can appeal to some of the existing classification theorems to identify G wi