๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Testing Matrix Groups for Primitivity

โœ Scribed by Derek F. Holt; C.R. Leedham-Green; E.A. O'Brien; Sarah Rees


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
206 KB
Volume
184
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis


We describe an algorithm which seeks to decide whether or not a matrix group defined over a finite field acts to preserve blocks of imprimitivity and, if so, to find a block system. Implementations of the algorithm are publicly available.


๐Ÿ“œ SIMILAR VOLUMES


Asymptotic Results for Primitive Permuta
โœ L Pyber; A Shalev ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 216 KB

We prove that the number of conjugacy classes of primitive permutation groups cลฝ n. ## ลฝ . of degree n is at most n , where n denotes the maximal exponent occurring in the prime factorization of n. This result is applied to investigating maximal subgroup growth of infinite groups. We then proceed

Isomorphism testing for p-groups
โœ E.A. O'Brien ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 478 KB

We describe the theoretical and practical details of an algorithm which can be used to decide whether two given presentations for finite \(p\)-groups present isomorphic groups. The approach adopted is to construct a canonical presentation for each group. A description of the automorphism group of th

Isomorphism testing for p-groups
โœ E.A. O'Brien ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 451 KB
Asymptotic Results for Primitive Permuta
โœ A. Lucchini; F. Menegazzo; M. Morigi ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 135 KB

A well-developed branch of asymptotic group theory studies the properties of classes of linear and permutation groups as functions of their degree. We refer to the surveys of Cameron [4] and Pyber [17,18] and the recent paper by Pyber and Shalev [19] for a detailed exposition of this subject. In thi

Constructing Permutation Representations
โœ GENE COOPERMAN; LARRY FINKELSTEIN; MICHAEL TSELMAN; BRYANT YORK ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 465 KB

New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutat

Matrix Generators for the Orthogonal Gro
โœ L.J. Rylands; D.E. Taylor ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 395 KB

In 1962 Steinberg gave pairs of generators for all finite simple groups of Lie type. In this paper, for each finite orthogonal group we provide a pair of matrices which generate its derived group: the matrices correspond to Steinberg's generators modulo the centre. These generators have been impleme