All Questions
Tagged with applications group-theory
28
questions
2
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0
answers
66
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A first course in abstract algebra Fraleigh 8th ed Section 5 Exercise 65
Cracker Barrel Restaurants place a puzzle called “Jump All But One Game” at each table. The puzzle starts with golf tees arranged in a triangle as in Figure 5.29a where the presence of a tee is noted ...
2
votes
1
answer
73
views
Books on the applications of group theory.
Background:
Applications abound!
I am aware of applications of group theory in general:
cryptography.
physics.
chemistry.
virology.
computer science.
anywhere there's symmetry.
Outside those broad ...
3
votes
1
answer
79
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A real-world example for a centralizer property
Context: I'm re-studying basic group theory and looking for "real-world" examples/puzzles that can be translated into abstract group theoretic statements. By real-world I mean not something ...
2
votes
0
answers
76
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Applications of group theory/abstract algebra [duplicate]
Before voting down, I would this text to be read.
This is not exactly a question regarding a hint to solve an exercise of a list or an exam, but a question involving the possible utility of which is ...
5
votes
2
answers
193
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Application of nonfamous finite groups in computer science [closed]
I have searched a lot about applications of finite groups in computer science. Most of the results include:
Finite fields or groups of numbers coprime to $n$ which are widely used in cryptography and ...
0
votes
0
answers
58
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On the group action $\psi: X \times \Bbb R^*_+ \to X$
Today I revisited the concept of a group action with someone. I recalled the definition of a "flow" which is a group action of the additive group of real numbers on the set $X:$
$$\varphi: X ...
2
votes
1
answer
69
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Show that $\prod_{i=1}^{n}\text{Aut}(G_i)\to \text{Aut}\Big(\prod_{i=1}^{n}G_i\Big)$ is injective
Let $G_1,...,G_n$ be groups. Show that there exist an injective morphism $\xi:$$\prod_{i=1}^{n}\text{Aut}(G_i)\to \text{Aut}\Big(\prod_{i=1}^{n}G_i\Big)$. I would like to know if my proof holds, ...
-1
votes
1
answer
272
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What is the real life application of group theory other than coding and cryptography [duplicate]
What is the real life application of group theory other than coding and cryptography if any and how can one apply group theory to them.
0
votes
1
answer
164
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Elementary group theory applications [duplicate]
I'm taking an algebraic structures class and we are doing a lot of work involving group theory. Specifically, dihedral groups, abelian groups, isomorphisms, cyclic groups, and others. I'm finding it ...
1
vote
1
answer
551
views
What are the applications of nilpotent elements/nilpotent ideals?
As I am doing exercises related to group and ring theory I constantly see questions regarding nilpotent elements/ideals/groups. However, I have yet to see any practical use of them in theory, but I ...
0
votes
1
answer
82
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Topological groups vs regular groups [duplicate]
I know group theory and I'm familiar with the concept and definition of Group.
Today I was reading an article about topology and discoverer the concept of "topological group". I read the ...
5
votes
3
answers
2k
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Real-world applications of fields, rings and groups in linear algebra.
Real-world applications of fields, rings and groups in linear algebra.
A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact ...
2
votes
3
answers
374
views
What are some applications of subdirect product?
I have studied direct products. I know a few applications of direct products, like group isomorphism, etc. What are some applications of sub-direct product of groups?
3
votes
0
answers
87
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Cyclic/non-cyclic groups and their applications in credit card/ smart card security
Can someone point me to resources on "Cyclic/non-cyclic groups and their applications in credit card/ smart card security"
What I have right now is some things on
Diffie-Hellman Key exchange ...
4
votes
2
answers
753
views
Simple applications of Lie algebra in group theory
In his book Lie Algebra, Jacobson gives a motivation for Lie algebra as a tool used in a difficult problem in group theory - Burnside's problem.
I was wondering if there is any simple/elementary ...
1
vote
0
answers
378
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Application of Jordan–Hölder theorem
Jordan–Hölder theorem can be used to prove the fundamental theorem of arithmetic. But I can only prove the uniqueness part of the theorem with Jordan–Hölder theorem. That every composite number is ...
6
votes
1
answer
2k
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Applications of group theory to classical mechanics
Today, a friend and I solved a classical mechanics problem using group theory. The problem was the following:
Around a circumference, there are $N$ children evenly spaced. In the center, there is a ...
0
votes
2
answers
128
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What are the other methods used to prove that a homomorphism is bijective?
The motivation can be found in: Show that $ℤ^{m}$ is a subgroup (and a free abelian group) of $ℤ^{n}$ for all $m≤n$.
In a specified problem related to a dynamical system the only possibility is $m=n$...
2
votes
2
answers
811
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What is the difference between the words chord, tangent in (a) and (b)?
(a) If a function $g$ is continuous on the closed interval $[u,v]$, where $u<v$, and differentiable on the open interval $(u,v)$, then there exists a point $c$ in $(u,v)$ such that
$$g(v)=g(u)+g′(...
3
votes
1
answer
1k
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Graph (or Group) in Astronomy
Is there an application of graph theory (or group theory) in astronomy. If there is, refer me some references.
6
votes
1
answer
303
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Quote on the Littlewood-Richardson Rule
In Gordon James's paper "The representation Theory of the Symmetric Group" he says
"The author was once told that the Littlewood���Richardson rule helped to get men on the moon but was not proved until ...
4
votes
4
answers
3k
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Applications of group theory to geometry
What are the applications of group theory to geometry? Where can I know more about these applications?
116
votes
8
answers
36k
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Are there real world applications of finite group theory?
I would like to know whether there are examples where finite group theory can be directly applied to solve real world problems outside of mathematics. (Sufficiently applied mathematics such as ...
2
votes
0
answers
92
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Molecular vibrations and a generalisation of Wigner's rule for (non-finite) compact groups
years student of mathematics and write my script for my bachelor. The topic is "Representations of groups and applications in physics". I understand the representations very good but now i want to ...
12
votes
3
answers
7k
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What are applications of rings & groups?
I am following a course in basic algebra, and we have covered rings & groups in class, but I am having trouble visualising them. Are there applications of group &/or ring theory that can be ...
6
votes
3
answers
5k
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Group theory applications along with a solved example
As I asked in previous question, I am very curious about applying Group theory. Still I have doubts about how I can apply group theory. I know about formal definitions and I can able to solve and ...
38
votes
8
answers
9k
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Applications of the wreath product?
We recently went through the wreath product in my group theory class, but the definition still seems a bit unmotivated to me. The two reasons I can see for it are 1) it allows us to construct new ...
6
votes
4
answers
632
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recommend paper on application of group theory
Application field can vary from biology\biochemistry, to computer science\coding theory, the more unexpected a connection to a field, the better. And paper preferably should be not very large one.
...