Construction of Large Permutation Representations for Matrix Groups

Michael Weller
Additional contact information
Michael Weller: University of Essen, Institute for Experimental Mathematics

A chapter in High Performance Computing in Science and Engineering ’98, 1999, pp 430-452 from Springer

Abstract: Abstract This article describes the general computational tools for a new proof of the existence of the large sporadic simple Janko group J 4 [10] given by Cooperman, Lempken, Michler and the author [7] which is independent of Norton [12] and Benson [1]. Its basic step requires a generalization of the Cooperman, Finkelstein, Tselman and York algorithm [6] transforming a matrix group into a permutation group. An efficient implementation of this algorithm on high performance parallel computers is described. Another general algorithm is given for the construction of representatives of the double cosets of the stabilizer of this permutation representation. It is then used to compute a base and strong generating set for the permutation group. In particular, we obtain an algorithm for computing the group order of a large matrix subgroup of GL n (q), provided we are given enough computational means. It is applied to the subgroup G = 〈x, y〉

Keywords: Hash Function; Maximal Subgroup; Permutation Group; Hash Table; Orbit Element (search for similar items in EconPapers)
Date: 1999
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-58600-2_41

Ordering information: This item can be ordered from
http://www.springer.com/9783642586002

DOI: 10.1007/978-3-642-58600-2_41

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().