𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Number of Homomorphisms from a Finite Group to a General Linear Group

✍ Scribed by Naoki Chigira; Yugen Takegahara; Tomoyuki Yoshida

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
144 KB
Volume
232
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We study the number of homomorphisms from a finite group to a general linear group over a finite field. In particular, we give a generating function of such numbers. Then the Rogers-Ramanujan identities are applicable.

πŸ“œ SIMILAR VOLUMES

On the Number of Generators and Composit
On the Number of Generators and Composition Length of Finite Linear Groups
✍ A Lucchini; F Menegazzo; M Morigi πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 151 KB

In 1991 Dixon and Kovacs 8 showed that for each field K which has finite degree over its prime subfield there is a number d such that every K finite nilpotent irreducible linear group of degree n G 2 over K can be w x wx ' generated by d nr log n elements. Afterwards Bryant et al. 3 proved K ' d G F

On the Number of Generators of Finite Im
On the Number of Generators of Finite Images of Free Products of Finite Groups
✍ Andrea Lucchini πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 108 KB

We prove that the analog of the Grushko-Neumann theorem does not hold for profinite free products of profinite groups. To do that we bound the number of generators of a finite group generated by a family of subgroups of pairwise coprime orders.

On the -hypercentre of a finite group
On the -hypercentre of a finite group
✍ Adolfo Ballester–Bolinches; Xaro Soler–EscrivΓ  πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 108 KB

## Abstract The main objective of this paper is to study and describe the hypercentre of a finite group associated with saturated formations, in terms of some subgroup embedding properties related to permutability. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the Number of Conjugacy Classes of Ο€-
On the Number of Conjugacy Classes of Ο€-Elements in a Finite Group
✍ Burkhard KΓΌlshammer; Geoffrey R. Robinson πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 136 KB

Let G be a finite group and a set of primes. In this note we will prove Ε½ . two results on the local control of k G, , the number of conjugacy w x classes of -elements in G. Our results will generalize earlier ones in 8 , w x w x 9 , and 3 . Ε½ . Ε½ . In the following, we denote by F F G the poset of