# vwxyzjn/Abstract_Algebra_Finite_Group_Generator

A brute force program that enumerates all possible permutations of binary operations on a given set.
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app.py

# Abstract_Algebra_Finite_Group_Generator

This is brute force program that enumerates all possible permutations of binary operations on a given set. It further investigate which permutation, along with the given set, defines a valid group.

A group < G, * > is a set G, closed under a binary operation *, such that the following axioms are satisfied:

• For all $a,b,c \in G$, we have
• $(a * b) * c = a * (b * c) • There is an element$e$in$G$such that for all$x \in G$, •$e * x = x * e = x$•$e$is the identity element for * • Corresponding to each$a \in G$, there is an element$a'$in$G$such that •$a * a' = a' * a = e$•$a'$is called the inverse of$a\$

you may use

check_group([0,1,2])
#check_group([0,1,2,3]) # this will take a long time to run

to enumerate all the order 3 finite groups and return only the valid ones.