All Questions
Tagged with terminology group-theory
11
questions
1
vote
2
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206
views
Why is it called a group action?
A group action has two laws which roughly correspond to associativity and identity
$
\phi : (G : \textrm{Group}) \times (S : \textrm{Set}) \rightarrow S \\
\forall a, b : G . \forall c : S. \phi(a,\...
7
votes
1
answer
350
views
Why is the number of elements in a group called "order"?
This is a question that I have for a long time, Maybe it is something silly, but I really want to know. Why is the number of elements in a group called "order"? I mean, the word "order&...
- 181
0
votes
0
answers
111
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History of PSL(2,Z)
I want to know the mathematician who named PSL(2,Z) as the modular group first. Also, I would be pleased if someone suggest to me some papers about the history of the modular group. Thanks a lot in ...
- 1
3
votes
0
answers
95
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Origin of the term 'index of a subgroup'
The index of a subgroup $H$ in a group $G$ is the number of distinct cosets of $H$ in $G$.
Why did someone decide to call this an 'index'?
- 151
2
votes
0
answers
108
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Why are faithful actions called faithful and who first called them faithful?
This is a cross post from MSE
I want to know why are faithful actions called faithful and who first called them faithful?
Definition: An action $G$ on $X$ is faithful when ${g_1 \neq g_2 \Rightarrow ...
- 171
10
votes
1
answer
550
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How did the terms "center" and "centralizer" come up in group theory?
Usually the word center means the center of a circle. I have encountered the word center in group theory, but do not see any connection with the center of a circle. I think the history of group theory ...
- 203
2
votes
0
answers
717
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What does the "G" for the similitude groups stand for?
When we have a bilinear symmetric/ bilinear anti-symmetric/hermitian form $b$ on a real/complex vector space $V$, one can consider the group of invertible matrices $A \in GL(V)$ which respect $b$, ...
- 395
2
votes
1
answer
608
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History of group theory character tables (as used in physics and chemistry)
Does anyone know who started using the symbols A, B, E, T (First column, left) for showing irreducible representations of symmetry groups? In older maths books I see capital gamma. Herein A= totally ...
- 4,184
2
votes
1
answer
664
views
Earliest known usage of letter gamma "Γ" for reducible representation in group theory
Does any know the earliest known usage of the Greek letter gamma for showing a reducible representation of a group? This symbolism is commonly used in character tables in chemical applications of ...
- 4,184
9
votes
0
answers
460
views
Whence “homomorphism”, “homomorphic”?
The kernel question leads to another : Today, homomorphism (resp. isomorphism) means what Jordan (1870) had called isomorphism (resp. holoedric isomorphism). How did the switch happen?
“Homomorphic” ...
- 7,764
3
votes
0
answers
301
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History of the Wreath product
Why is the wreath product so named?
If possible, please provide a citation.
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