Necessary condition for isomorphism but not sufficient

[aidevnn]

https://github.com/aidevnn/FastGoat/blob/07415a057d81a809c340d3c6b537f32e591e3d4f/FastGoat/ConcreteGroup.cs#L139-L144

This condition is necessary for isomorphic groups but it is not sufficient. A counter-example is between groups (C8 : C4) and (C4 : C8) as shown in Examples folder.

https://github.com/aidevnn/FastGoat/blob/07415a057d81a809c340d3c6b537f32e591e3d4f/FastGoat/Examples/GroupOrder32C4C8.cs#L14-L35

which will output

|C8 x: C4| = 32
Type        NonAbelianGroup
BaseGroup    Z8 x Z4
NormalGroup  |C8| = 8
ActionGroup  |C4| = 4

Actions
g=0 y(g) = (0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7)
g=1 y(g) = (0->0, 1->5, 2->2, 3->7, 4->4, 5->1, 6->6, 7->3)
g=2 y(g) = (0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7)
g=3 y(g) = (0->0, 1->5, 2->2, 3->7, 4->4, 5->1, 6->6, 7->3)

Sorted Orders C8 x: C4 : (1, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8)
|C4 x: C8| = 32
Type        NonAbelianGroup
BaseGroup    Z4 x Z8
NormalGroup  |C4| = 4
ActionGroup  |C8| = 8

Actions
g=0 y(g) = (0->0, 1->1, 2->2, 3->3)
g=1 y(g) = (0->0, 1->3, 2->2, 3->1)
g=2 y(g) = (0->0, 1->1, 2->2, 3->3)
g=3 y(g) = (0->0, 1->3, 2->2, 3->1)
g=4 y(g) = (0->0, 1->1, 2->2, 3->3)
g=5 y(g) = (0->0, 1->3, 2->2, 3->1)
g=6 y(g) = (0->0, 1->1, 2->2, 3->3)
g=7 y(g) = (0->0, 1->3, 2->2, 3->1)

Sorted Orders C4 x: C8 : (1, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8)

Isomorphic C4 x: C8 C8 x: C4 True
Homomorphisms Count = 256
Isomorphisms  Count = 0

And then, this example also provide how to check computationally isomorphism between two group.