Small Groups Library
The group theoretical computer algebra system GAP contains the "Small Groups library" which provides access to descriptions of small order groups. The groups are listed up to isomorphism. At present, the library contains the following groups:
- those of order at most 2000, except for order 1024 (423164062 groups in the library; the ones of order 1024 had to be skipped, as there are an additional 49487365422 nonisomorphic 2-groups of order 1024.);
- those of cubefree order at most 50000 (395 703 groups);
- those of squarefree order;
- those of order for n at most 6 and p prime;
- those of order for p = 3,5,7,11 (907 489 groups);
- those of order qn×p where qn divides 28, 36, 55 or 74 and p is an arbitrary prime which differs from q;
- those whose orders factorise into at most 3 primes.
It contains explicit descriptions of the available groups in computer readable format.
Read more about this topic: List Of Small Groups
Famous quotes containing the words small, groups and/or library:
“The future of humanity is uncertain, even in the most prosperous countries, and the quality of life deteriorates; and yet I believe that what is being discovered about the infinitely large and infinitely small is sufficient to absolve this end of the century and millennium. What a very few are acquiring in knowledge of the physical world will perhaps cause this period not to be judged as a pure return of barbarism.”
—Primo Levi (1919–1987)
“Under weak government, in a wide, thinly populated country, in the struggle against the raw natural environment and with the free play of economic forces, unified social groups become the transmitters of culture.”
—Johan Huizinga (1872–1945)
“I view askance a book that remains undisturbed for a year. Oughtn’t it to have a ticket of leave? I think I may safely say no book in my library remains unopened a year at a time, except my own works and Tennyson’s.”
—Carolyn Wells (1862–1942)