We show that residually finite or word hyperbolic groups which can be decomposed as a finite union of double cosets of a cyclic subgroup are necessarily virtually cyclic, and we apply this result to the study of Frobenius permutation groups. We show that in general, finite double coset decomposition
Enumeration of double cosets
β Scribed by Robert H. Gilman
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 313 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0022-4049
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We discuss the use of orbit-stabilizer and orbit reduction techniques for computing representatives of double cosets in finite soluble groups given by a polycyclic presentation.
Coset enumeration, like GrΓΆbner bases, is a notoriously difficult algorithm to parallelize. We demonstrate a successful shared memory parallelization achieving a seven times speedup on an Origin 2000 CC-NUMA computer using 16 CPUs. We take as a testbed, an enumeration of Lyons's group (8 835 156 cos
## COMPLETE ENUMERATIONS AND DOUBLE SEQUENCES l ) by M. ADRIAN CARPENTIER in Notre Dame, Indiana (U.S.A.) A. E. MALCEV has defined complete enumerations and shown a correspondence between these and universal sequences of sets [3], this latter concept being equivalent to creativity for disjoint re