✦ LIBER ✦

On the Finite Simple Groups All of Whose 2-Local Subgroups Are Solvable

✍ Scribed by Makoto Hayashi; Yasuhiko Tanaka

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 177 KB
Volume: 210
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7587

No coin nor oath required. For personal study only.

✦ Synopsis

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 with one of the known simple groups. Hence Ž . we can assume that 3 occurs in Theorem 2, and then G satisfies the assumption of Theorem 1. Once Theorem 1 is proved, we can know the structures of the subgroups S, H, K by Theorem 3, and then identify G with one of the known simple groups, appealing again to some classification theorems.

📜 SIMILAR VOLUMES

Sylow Subgroups Which Are Maximal in the

Sylow Subgroups Which Are Maximal in the Universal Locally Finite Group of Philip Hall

✍ Marianna Dalle Molle 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 104 KB

For every prime p, we construct a subgroup of Philip Hall's universal locally finite group which is both maximal and a p-group. This provides an example of a simple locally finite group with a maximal subgroup which is locally nilpotent. ᮊ 1999 Academic Press G theme to a locally finite group G, fin

On Odd Degree Parts of Cohomology of Spo

On Odd Degree Parts of Cohomology of Sporadic Simple Groups Whose Sylowp-Subgroup Is the Extra-Specialp-Group of Orderp3

✍ Nobuaki Yagita 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 241 KB

On the Irreducible Characters of a Sylow

On the Irreducible Characters of a Sylow 2-Subgroup of the Finite Symplectic Group in Characteristic 2

✍ Rod Gow; Martin Marjoram; Andrea Previtali 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 124 KB

We show that if P is a Sylow 2-subgroup of the finite symplectic group m Ž . ## Sp q , where q is a power of 2, then P has irreducible complex characters of 2 m m yt mŽ my1.r2 w x degree 2 q , where t is any integer satisfying 0 F t F mr2 , and that q mŽ my1.r2 is the largest possible degree of a

On the Construction of the Finite Simple

On the Construction of the Finite Simple Groups with a Given Centralizer of a 2-Central Involution

✍ Gerhard O. Michler 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 193 KB

## dedicated to helmut wielandt on the occasion of his 90th birthday Let H be a finite group having center Z H of even order. By the classical Brauer-Fowler theorem there can be only finitely many non-isomorphic simple groups G which contain a 2-central involution t for which C G t ∼ = H. In this