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, copy the library file, tinygroups.m (or in zip format), into your maple library directory (evaluate the "libname" variable to see where this is) or the directory containing your worksheets.
The package provides three variables, each of which is a nested list. The first index "n" for each variable is the group size ("order" of the group), and the second index "k" determines which of the groups of order n to use.
* TGNames: the names of the groups
- TG[n][k] is the kth group of order n and TGName[n][k] is its name
- the names are taken from the GAP smallgroups package
* TGElts: the names of the elements of the groups
- we index the group elements of TG[n][k] from 1 to n
- TGElts[n][k][i] is the name of the ith element of TG[n][k]
* TG: a list of the group operation tables for the groups of size up to 60
- TG[n][k] is an n-by-n table of the group operation for the kth group of order n, with elements indexed from 1 to n
- specifically, TG[n][k][i][j] is the value of the group operation applied to i and j in the kth group of order n
The identity of each group is the element indexed 1.
Here are some examples: