Is there a Program that Identifies and Names Subgroups of a Defined Group?

[krishna mohan]

Hi...

I need a program that can give me all the subgroups of a group that I define. I also need it to give me the names of the subgroups as per some predefined library.


I tried GAP. It gives me the subgroups, but each subgroup is represented by a list of generators. There seems to be no way to make it print a name for the subgroups, like say S4 for symmetric group of four elements.

In fact, if I give the generators of S4 as input, it cannot identify it and give an output stating that it is S4.

Any suggestions?

 

[mmwave]

Hello, thank you for reaching out. It sounds like you are looking for a program that can not only list the subgroups of a defined group, but also provide their corresponding names according to a library. I would recommend checking out the program Magma. It has a subgroup command that can list the subgroups of a group and also has a library of predefined group names that it can recognize and label the subgroups accordingly. Additionally, Magma has a built-in function for recognizing and labeling symmetric groups, so it should be able to correctly identify and label S4 if given its generators as input. I hope this helps and good luck with your research!