All Questions
Tagged with applications group-theory
28
questions
2
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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 ...
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votes
1
answer
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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 ...
- 45.8k
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 ...
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2
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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 ...
- 1,361
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
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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 $X:$
$$\varphi: X ...
- 756
2
votes
1
answer
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Show that $\prod_{i=1}^{n}\text{Aut}(G_i)\to \text{Aut}\Big(\prod_{i=1}^{n}G_i\Big)$ is injective
Let $G_1,...,G_n$ be groups. Show that there exist an injective morphism $\xi:$$\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, ...
- 1,677
-1
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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 ...
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1
vote
1
answer
551
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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 ...
- 71
0
votes
1
answer
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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 ...
- 4,962
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 ...
- 1,197
2
votes
3
answers
374
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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
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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 ...
- 429
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0
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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 ...
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2
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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 $m=n$...
- 3,021
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′(...
- 3,021
3
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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.
- 207
6
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1
answer
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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 ...
- 17.5k
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?
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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 ...
- 27.2k
2
votes
0
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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
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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 ...
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3
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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 ...
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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 ...
user8420
6
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4
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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.
...
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