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Questions tagged [finite-group-theory]

Finite group theory is a branch of abstract algebra concerned with the properties of a multiply-like operation on finite sets. Applications include error correcting codes and cryptography.

Finite group theory is a branch of abstract algebra concerned with the properties of a multiply-like operation on finite sets. Practical applications are found in error correcting codes , cryptography, chemistry, physics, and other fields.

Questions regarding finite group theory are expected to involve programming to be on-topic on this site.

Wikipedia: Group Theory

Are there real-world applications of finite group theory? on Math Stack Exchange

Sage python module and group theory

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Minimum cost factoring in abelian groups

I have a certain optimization problem, and I'm wondering if there is a clever approach for solving it. (This may well have been extensively studied and I just don't know what name to look it up under.) I have a (EDIT: free) finitely generated…
Doug McClean
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Group theory and Python

How do you write a Python code to check if the operation ∗ on the set {0,1,..,n−1} defined by a Cayley table is associative or not. My attempted code is: def is_associative_cayley_table(table): if not is_cayley_table(table): return…
Scream98
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How to check that concrete method is respecting type-hinting for an abstract method

This is a two-part question, but the second part is dependent on the first part. For educational purposes, I am trying to implement an abstract base class and test suite for groups (the concept from abstract algebra). Part of the definition of an…
R Hill
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Modular run-length encoding

Question How to implement a run length encoding modulus n>=1? For n=4, considering the inputAAABBBBABCCCCBBBDAAA, we want an output of [('D', 1), ('A', 3)]. Note the long-distance merging due to the modulus operation. See Explanation.…
hyiltiz
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Elementary abelian groups

I just read on Wikipedia about elementary abelian groups which appear to be related to bit fields. I'd be grateful if someone could explain me this particular paragraph as I strive to fully master bit fields.
Michael Blurb
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Totality and searching for elements in Streams

I want a find function for Streams of size-bounded types which is analogous to the find functions for Lists and Vects. total find : MaxBound a => (a -> Bool) -> Stream a -> Maybe a The challenge is it to make it: be total consume no more than…
Sage Mitchell
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SAGE implementation of discrete logarithm in subgroup of group of units

This is a question related to this one. Briefly, in ElGammal cryptosystem with underlying group the group of units modulo a prime number p I'm told to find a subgroup of index 2 to solve discrete logarithm problem in order to break the system.…
user1868607
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Generating all words of length N (N being prime) excluding isomorphic ones

I would like to efficiently generate all words length N (N is prime) excluding isomorphic one. Word A isomorphic to word B if there is an Automorphism for Finite Cyclic group with N elements that convert word A to the word B. Let V - is an alphabet…
Alexey Krugovets
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In CGAL, can one convert a triangulation in more than three dimensions to a polytope?

If this question would be more appropriate on a related site, let me know, and I'd be happy to move it. I have 165 vertices in ℤ11, all of which are at a distance of √8 from the origin and are extreme points on their corresponding convex hull. …
OzoneNerd
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Most natural datastructure to store a permutation of distinct elements?

One easy way to store a permutation of a sequence of distinct elements is as a string (or list) like, "acb" which is clearly a permutation of "abc". However, if I use a string to represent my permutation, I will end up with the possibility of…
Display Name
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SymPy Permutation groups parity not working as expected

I've implemented a Rubik's cube using permutations of Tuples. The cube with no changes is represented as (0, 1, 2, ... , 45, 46, 47). To apply a 'turn' to the cube the numbers are shuffled around. I've pretty fully tested all of my turns to the…
elliot_martin18
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Any algorithm related to Rubik's Cube

I got an interesting idea yesterday. Imagine you have a Rubik's Cube with already same colours on each face. Now, if I twist it once and I know how I twist it, I could always recover the cube to its original by reversing this step. If I twist twice,…
Ryan
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use the functions defined in the class

I'm writing a program for representation of finite groups and simple operations on their elements. I wrote most of the functionality which I need, for example inverse elements, generators, checking if subset is subgroup etc. Unfortunately all my…
user4638556
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Determine if (*,G) forms an associative group in group theory

Lets say I have a group G={a,b,e} where a,b are arbitrary elements and e denotes the neutral element. I came up with a certain Cayley table and want to verify that what I have done is right by checking the associativity. That means I want to check…
Spaced
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Dafny recursive trigger debugging

Following up from a previous question here. I'm trying to extend my definition of an abstract power for all integers. I thought I setup the triggers correctly but I'm still running into recursive triggers endlessly verifying. Is there a better way…
Hath995
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