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This is a page on GAP 3, which is still available, but no longer supported. The present version is GAP 4  (See  Status of GAP 3).

GAP 3 Share Package "dce"

DCE: Double Coset Enumerator

Share package since release 3.4, about December 1995.
This package has not yet been transferred to or replaced in GAP 4. You can use it only in GAP 3.


Steve Linton.


Language: GAP 3
Operating system: Any
Current version: 1.0 (in the 3.4.4 distribution)


Double Coset Enumeration (DCE) can be seen either as a space- (and time-) saving variant of ordinary Coset Enumeration (the Todd-Coxeter procedure), as a way of constructing finite quotients of HNN-extensions of known groups or as a way of constructing groups given by symmetric presentations in a sense defined by Robert Curtis. A double coset enumeration works with a finitely-presented group G, a finitely generated subgroup H (given by generators) and a finite subgroup K, given explicitly, usually as a permutation group. The action of G on the cosets of H divides into orbits under K, and is constructed as such, using only a relatively small amount of information for each orbit.


A DCE manual is given in chapter 61 of the GAP 3 manual.

Contact address

Steve Linton
School of Computer Science
University of St Andrews
North Haugh
St Andrews, Fife, KY16 9SS