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 ...
- 21
2
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 ...
- 45.7k
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 ...
- 145
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
answers
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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 $X:$
$$\varphi: X ...
- 946
2
votes
1
answer
69
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Show that $\prod_{i=1}^{n}\text{Aut}(G_i)\to \text{Aut}\Big(\prod_{i=1}^{n}G_i\Big)$ is injective
Let $G_1,...,G_n$ be groups. Show that there exist an injective morphism $\xi:$$\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, ...
- 1,677
-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 ...
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1
vote
1
answer
545
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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
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 ...
- 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
370
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
749
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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 ...
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