CoCalc Public FilesFinalCode.sagewsOpen with one click!
Authors: Bret Benesh, Jordan Schultze, Yijiao Tian
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def givequotients(i,j): mygroup = gap.SmallGroup(i,j) mysubgps = gap.NormalSubgroups(mygroup) for k in range (1,len(mysubgps) + 1): myquotient = gap.FactorGroup(mygroup,mysubgps[k]) print gap.StructureDescription(myquotient) def findgroups(lower,upper): for i in range(lower,upper + 1): numbergroups = gap.NumberSmallGroups(i) for j in range(1,numbergroups + 1): mygroup = gap.SmallGroup(i,j) quotientFlag=True #print '---------' if not gap.IsAbelian(mygroup): mysubgps = gap.NormalSubgroups(mygroup) for k in range(2,len(mysubgps)): myquotient = gap.FactorGroup(mygroup,mysubgps[k]) if not gap.IsAbelian(myquotient): quotientFlag = False break if quotientFlag == true: print gap.StructureDescription(mygroup) , " - GAP Group ID:" , (i,j) #findgroups(1,60)p.StructureDescription(gap.SmallGroup(16,2)) findgroups(1,10)
C4 x C4 S3 - GAP Group ID: (6, 1) D8 - GAP Group ID: (8, 3) Q8 - GAP Group ID: (8, 4) D10 - GAP Group ID: (10, 1)
givequotients(6,1)
S3 C2 1
done":true}
givequotients(6,1)
S3 C2 1