CoCalc Shared Filesttest.sagews
Author: Killian O'Brien
Views : 54
A4 = AlternatingGroup(4)
A4

Alternating group of order 4!/2 as a permutation group
A4.subgroups()

[Subgroup generated by [()] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,2)(3,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,4)(2,3)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(2,4,3)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,2,3)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,4,2)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,3,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,2)(3,4), (1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(2,4,3), (1,2)(3,4), (1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group)]
[x for x in A4]

[(), (1,3)(2,4), (1,2)(3,4), (1,4)(2,3), (2,4,3), (1,3,4), (1,2,3), (1,4,2), (2,3,4), (1,3,2), (1,2,4), (1,4,3)]
[(x,x.order()) for x in A4]

[((), 1), ((1,3)(2,4), 2), ((1,2)(3,4), 2), ((1,4)(2,3), 2), ((2,4,3), 3), ((1,3,4), 3), ((1,2,3), 3), ((1,4,2), 3), ((2,3,4), 3), ((1,3,2), 3), ((1,2,4), 3), ((1,4,3), 3)]
y=A4("(1,3)(2,4)")
y

(1,3)(2,4)
H = A4.subgroup([y])
H
[x for x in H]

Subgroup generated by [(1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group) [(), (1,3)(2,4)]
[h for h in H]

[(), (1,2)(3,4)]