In this paper G denotes a finite group. As is well known, the converse of Lagrange's theorem in group theory does not hold. That is, given a finite group G of order n, and given a divisor d of n, G need not have a subgroup of order d. Indeed, a celebrated theorem of P. Hall states that it suffices t
On subgroups of finite solvable groups II
β Scribed by Avinoam Mann
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 466 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We present practical algorithms to compute subgroups such as Hall systems, system normalizers, F-normalizers and F-covering subgroups in finite solvable groups. An application is an algorithm to calculate head complements in finite solvable groups; that is, complements which are closely related to m
## 2 1 2 1 2 4 2 Ε½ . gam, or a F 2 -amalgam. ## 4 Let G be a nonabelian simple group satisfying the assumption of the Ε½ . Main Theorem. Then G satisfies the assumption of Theorem 2. If 1 or Ε½ . 2 occurs in Theorem 2, we can appeal to some of the existing classification theorems to identify G wi