CoCalc Public FilesFinalCode.sagews
Authors: Bret Benesh, Jordan Schultze, Yijiao Tian
Views : 22
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