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Manuscript Title: Computation of group tables for the symmetric groups.
Authors: M.F. Soto Jr., R. Mirman
Program title: SYMGRPTB
Catalogue identifier: AAMC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)81
Programming language: PL/1.
Computer: IBM 3033.
Operating system: OS/MVT/ASP.
RAM: 228K words
Word size: 8
Peripherals: magnetic tape.
Keywords: General purpose, Algebras, Symmetric group, Group generators, Permutations, Group multiplication Table, Explicit construction.
Classification: 4.2.

Subprograms used:
Cat Id Title Reference
AAME_v1_0 SYMSTATS CPC 23(1981)95

Nature of problem:
To find explicitly the generators (permutations), and group multiplication tables for the symmetric groups.

Solution method:
The permutations of S(NMAX) are found by inserting parentheses, at positions determined by the computed row lengths of the frames, into the NMAX! strings of permutations of the numerals 1...NMAX. The group table is found by multiplying every pair of permutations, and searching for the permutation which is the same as their product.

The program can be used for any symmetric group, for which machine time and storage are available. However, for S(10) and above, there must be some modifications because the numbers then consist of two digits.

Running time:
Through S(4):20.71 s.