So it seems that GAP can do it..Identifying Groups in GAP: A Tutorial

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SUMMARY

The discussion centers on using GAP (Groups, Algorithms, Programming) for identifying subgroups of a defined group. Users expressed confusion regarding GAP's ability to name subgroups, specifically the symmetric group S4, when provided with its generators. It was clarified that GAP can indeed identify S4, contrary to some misleading tutorials. A helpful resource was shared, detailing the process of identifying groups within GAP.

PREREQUISITES
  • Familiarity with group theory concepts
  • Basic understanding of GAP (version not specified)
  • Knowledge of subgroup generation and representation
  • Access to GAP documentation and tutorials
NEXT STEPS
  • Review the tutorial on identifying groups in GAP from the provided link
  • Explore GAP's functions for subgroup generation and naming conventions
  • Learn about the structure and properties of the symmetric group S4
  • Investigate additional GAP resources for advanced group identification techniques
USEFUL FOR

Mathematicians, group theorists, and software developers working with GAP who need to identify and analyze subgroups effectively.

krishna mohan
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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?
 
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I'm confused..how can you say that it doesn't identify S4, when you give it generators of S4 and it tells you it's S4?
 
Yes..you are right..it is possible for GAP t o identify the group as S4..I had read some tutorials on the web which seemed to state that GAP did not have this capability..

But I got a reply at the GAP forum with this link..

http://www.math.colostate.edu/~hulpke/CGT/howtogap.pdf

It has a section named "Identifying Groups"...
 

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