Message Boards Message Boards


Calculating quotient groups and normal subgroups

Posted 5 months ago
0 Replies
0 Total Likes

Hello! I am trying to calculate all the quotient groups of the D4 group. I'm using the following Mathematica function to do so:

Q = FiniteGroupData[Group, "QuotientGroups"]

Which produces

{"Trivial", {"CyclicGroup", 2}, {"DihedralGroup", 
  2}, {"DihedralGroup", 4}}

I found the Normal subgroups as well, by doing

r = FiniteGroupData[Group, "NormalSubgroups"];
r = DeleteDuplicates[r, 
  IsomorphicGraphQ[FiniteGroupData[#1, "CycleGraph"], 
    FiniteGroupData[#2, "CycleGraph"]] &]

and got

{{"CyclicGroup", 1}, {"CyclicGroup", 2}, {"CyclicGroup", 
  4}, {"DihedralGroup", 2}, {"DihedralGroup", 4}}

According to the documentation centre the possible quotient groups, are obtained by finding the quotient with respect to normal subgroups, my question is if there's a way of knowing which normal subgroup was used to get each quotient group. For example, is there a way to know that the normal subgroup used to get the quotient group D2 was C2? I haven't found any way of doing this and could use some help, please.


Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract