Double coset enumeration of symmetrically generated groups

2004 ◽  
Vol 7 (2) ◽  
Author(s):  
John N. Bray ◽  
Robert T. Curtis
Keyword(s):  
Double Coset ◽  
Coset Enumeration

scholarly journals Double-coset enumeration algorithm for symmetrically generated groups

2005 ◽  
Vol 2005 (5) ◽  
pp. 699-715 ◽  
Author(s):  
Mohamed Sayed
Keyword(s):  
Double Coset ◽  
Computer Implementation ◽  
Enumeration Algorithm ◽  
Coset Enumeration

A double-coset enumeration algorithm for groups generated by symmetric sets of involutions together with its computer implementation is described.

scholarly journals Double coset enumeration

1991 ◽  
Vol 12 (4-5) ◽  
pp. 415-426 ◽  
Author(s):  
Stephen A. Linton
Keyword(s):  
Double Coset ◽  
Coset Enumeration

scholarly journals Computer aided determination of a Fibonacci group

1976 ◽  
Vol 15 (2) ◽  
pp. 297-305 ◽  
Author(s):  
George Havas
Keyword(s):  
Computer Aided ◽  
Group A ◽  
Coset Enumeration

The Fibonacci group F(2, 7) has been known to be cyclic of order 29 for about five years. This was first established by computer coset enumerations which exhibit only the result, without supporting proofs. The working in a coset enumeration actually contains proofs of many relations that hold in the group. A hand proof that F(2, 7) is cyclic of order 29, based on the working in computer coset enumerations, is presented here.

Double coset algebras

2014 ◽  
Vol 218 (11) ◽  
pp. 2081-2095 ◽  
Author(s):  
Robert May
Keyword(s):  
Double Coset

scholarly journals Some challenging group presentations

1999 ◽  
Vol 67 (2) ◽  
pp. 206-213 ◽  
Author(s):  
George Havas ◽  
Derek F. Holt ◽  
P. E. Kenne ◽  
Sarah Rees
Keyword(s):  
Finite Groups ◽  
Infinite Groups ◽  
Derived Length ◽  
Finitely Presented Group ◽  
Group Presentations ◽  
Coset Enumeration ◽  
Finitely Presented

AbstractWe study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are for infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bebdix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

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