#!/usr/bin/env python
# coding: utf-8

# In[1]:


from permutations import *
from groups import *


# ### Transitivity 
# 
# > n-transitive if X has at least n elements, and for all distinct x1, ..., xn and all distinct y1, ..., yn, there is a g in G such that g⋅xk = yk for 1 ≤ k ≤ n. A 2-transitive action is also called doubly transitive, a 3-transitive action is also called triply transitive, and so on. Such actions define interesting classes of subgroups in the symmetric groups: 2-transitive groups and more generally multiply transitive groups. The action of its symmetric group on a set with n elements is always n-transitive; the action of its alternating group is (n − 2)-transitive.
# 
# From [wikipedia](https://en.wikipedia.org/wiki/Group_action)

# In[2]:


x1,x2,x3,x4,x5 = 1,2,4,5,3
y1,y2,y3,y4,y5 = 3,2,1,4,5

S5 = create_symmetric_group_of_order(5)

for g in S5:
    if (g(x1) == y1) and (g(x2) == y2) and (g(x3) == y3) and (g(x4) == y4) and (g(x5) == y5):
        print(g)


# In[5]:


A5 = create_alternating_group_of_order(5)

for g in A5:
    if (g(x1) == y1) and (g(x2) == y2) and (g(x3) == y3) and (g(x4) == y4) and (g(x5) == y5):
        print(g) 

# None

for g in A5:
    if (g(x1) == y1) and (g(x2) == y2) and (g(x3) == y3):
        print(g)
        


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