Given a finite group G, we denote by l G the length of the longest chain of subgroups of G. We study whether certain sets of non-isomorphic finite simple groups S with bounded l S are finite or infinite. We prove, in particular, that there exists an infinite number of non-isomorphic non-abelian fini
Bounds on Orders of Finite Subgroups ofPGLn(K)
β Scribed by Eli Aljadeff; Jack Sonn
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 130 KB
- Volume
- 210
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
We characterize the pairs K, n , K a field, n a positive integer, for which there Ε½ . is a bound on the orders of finite subgroups of PGL K . Explicit bounds are given n in important cases. An application is made to the analogous problem for central simple K-algebras of degree n.
π SIMILAR VOLUMES
## Introduction. 1. p-groups with Small Groups of Operators. 2. The Number of Solutions to x p s 1 in a Sylow p-subgroup of the Symmetric Group. 3. p-groups with Maximal Elementary Subgroup of Order p 2 . 4. On the Maximal Order of Subgroups of Given Exponent in a p-group. ## 5. p-groups with
The following basic results on infinite locally finite subgroups of a free m-gener-Ε½ . ## 48 ator Burnside group B m, n of even exponent n, where m ) 1 and n G 2 , n is divisible by 2 9 , are obtained: A clear complete description of all infinite groups that Ε½ . Ε½ . are embeddable in B m, n as ma