The tinygroups package can be used to access basic information about small algebraic groups in Maple. It is a Maple version of the basic information of the "smallgroups" package for the GAP computer algebra system. Whereas the "smallgroups" package provides for groups up to size 2000, the tinygroups package only provides for groups up to size 60.

To install the package, download the file tinygroups.m into your maple library directory (e.g. "c:\Program Files\Maple 10\LIB" on a typical Windows installation).

The package provides three variables:

• TG: a list of the group operation tables for the groups of size up to 60
• TGNames: the names of the groups
• TGElements: the names of the elements of the groups

These variables are multi-dimensional arrays. The first index represents a group size, and the second index represents an index in the total number of nonisomorphic groups of that size. TGElements has a third index representing the name of the desired group element, and TG has a third and fourth so that TG[n][k][i][j] represents the result of adding the ith and jth elements of group TG[n][k]. The names are the same as those used by the "smallgroups" package. tinygroups indexes its elements from 1 to n where 1 is always the identity element.

Here is an example:

we just loaded the package

there are five groups of size 12

the out of these five groups, the third one is the alternating group on 4 elements

an addition table for A4.

for example, adding the 12th element to itself gives the 6th element

these are the names of the twelve elements, according to GAP