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Who was Richard Thompson?

I was only able to find fragmentary information on Thompson. A good starting point is his PhD thesis, which gives us his full name: Richard Joseph Thompson, Transformational Structure of Algebraic ...
njuffa's user avatar
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12 votes
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How and when did the dedicated study of locally compact groups begin?

The symbolic starting date is 1933, when Haar introduced left invariant measures and proved their existence on second-countable locally compact groups, see his Der Massbegriff in der Theorie der ...
Conifold's user avatar
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11 votes

Who was Richard Thompson?

To add to njuffa's answer. Thompson contributed to group theory, and algebraic logic. The original motivation for his calculations/constructs was algebraic logic. His thesis and all but two of his ...
Matt Brin's user avatar
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9 votes

What came first? The kernel from vector spaces or from group theory?

The quoted 1946 English edition of Pontryagin's 1938 book is not the first appearance of kernel. It's already in the first English edition (1939). It's earlier in e.g. 1938 papers of J. H. C. ...
Francois Ziegler's user avatar
8 votes

Representation theory in physics

Explicit applications of group representation to physics start with E. Noether, Invariante Variationsprobleme, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-...
Alexandre Eremenko's user avatar
8 votes

How did $SU(2)$ came into physics?

It came to physics a bit earlier than quantum mechanics. The homomorphism $SU(2)\to SO(3)$ was discovered by Cayley (1843), Hamilton (1847), and Klein (1875) in their pure mathematical studies, and ...
Alexandre Eremenko's user avatar
8 votes
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On the history of Haar measure

Cohn himself recommends historical notes at the end of sections 15, 16 of Abstract Harmonic Analysis by Hewitt and Ross, volume 1. Here is an excerpt: "Invariant integration on one or another ...
Conifold's user avatar
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8 votes
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Did Galois make use of the concept of a basis?

No, he did not. You are used to see Galois theory from the modern point of view, developed by Emmy Noether and two of her students: van der Waerden and Emil Artin. I suggest that you read B. Melvin ...
José Carlos Santos's user avatar
6 votes
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How did the terms "center" and "centralizer" come up in group theory?

The center (originally the central) seems to have appeared between the first and second edition of Burnside’s book (1897, §53 vs. 1911, §93) and more precisely in de Séguier (1904, §51): Ainsi l’...
Francois Ziegler's user avatar
6 votes

What are the origins of the study of symmetry as a subject in itself?

In my opinion, there are two separate questions being asked here. The expectation that the answer should concern 18th-19th century was not formulated in the statement of the question(s), although one ...
Margaret Friedland's user avatar
6 votes
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What are the origins of the study of symmetry as a subject in itself?

The traditional answer to questions on symmetry would be to point to Felix Klein's Erlangen Program as a way of systematizing the study of symmetry by focusing on the symmetries of a manifold as the ...
Mikhail Katz's user avatar
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5 votes

On the history of Haar measure

Try these references: Section 7.5 of History of Topology, edited by I. M. James. Section 2.2 of the chapter "Topological Features of Topological Groups" in Handbook of the History of General Topology,...
lhf's user avatar
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5 votes
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Who first identified the group structure of an elliptic curve?

In the 17th century Bachet and Fermat gave algebraic formulas for doubling a point on a cubic, and Newton showed how to do it in terms of chords and tangents. But that is as far as geometry progressed ...
Conifold's user avatar
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4 votes
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Intuitions for Frobenius' generalization of characters to nonabelian finite group given the historical context

We can’t redo the history. It just happens to be the case that Dedekind’s questions to Frobenius about group determinants were the original inspiration. It is not intuitive. Only later did Frobenius ...
KCd's user avatar
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4 votes

Why is the number of elements in a group called "order"?

I will promote my comment to an answer. The theory of permutations and permutation groups was the original (abstract) setting of group theory, and so the term originated there. I believe the reason ...
user1729's user avatar
  • 141
4 votes

First Use of the Short Exact Sequence

To narrow down your search: The lower bound is (probably) 1941. Dieudonne in his book "A history of Algebraic and Differential Topology" writes when discussing Gysin's exact sequence (which ...
Moishe Kohan's user avatar
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3 votes

What are the origins of the study of symmetry as a subject in itself?

On my opinion, there are two things which triggered this process in 19th cetury: Galois theory (and the work of his predecessors, like Lagrange and Cauchy). They introduced the notion of group. Work ...
Alexandre Eremenko's user avatar
3 votes
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First Use of the Short Exact Sequence

Although exact sequences appear in Hurewicz's short note from 1941, neither he nor other early authors (Eilenberg-Steenrod in 1945, Kelley-Pitcher in 1947) used short exact sequences, see Math SE, ...
Conifold's user avatar
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2 votes

Where can I find the early proofs for the simplicity of $\text{PSL}(n,q)$?

In 1831, Galois claimed simplicity when $n = 2$ and $q = p$ is a prime greater than $3$ without proof. The first paragraph here has references to later proofs of the result you ask about, first when $...
KCd's user avatar
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2 votes

Who was Richard Thompson?

Richard is a distant cousin of mine. He was living in Sunnyvale, CA when I met him about 15 years ago. He owns a house there, but he's pretty elderly and doesn't keep it up much. He's a bit eccentric.
J. S. Watson's user avatar
2 votes

Why is it called a group action?

What you define is monoid action. A group must act by permutations and the inverse element must act as inverse permutation. The second condition follows from the first and your two laws. Because the ...
markvs's user avatar
  • 882
2 votes

Why is it called a group action?

As you point out, the notion of an action is not particularly attached to that of a group. You can have actions from a more complex mathematical gadget like Lie algebra actions or ring actions or a ...
Mozibur Ullah's user avatar
2 votes
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A Survey of Modern Algebra, 1st Edition (Birkhoff and Mac Lane): The Direct Product

Well, my friend in Sheffield got a hold of a copy of the first edition over at the university library there, and, much to my annoyance, the book mentions neither direct products nor direct unions. ...
StormyTeacup's user avatar
2 votes
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History of group theory character tables (as used in physics and chemistry)

Mulliken credits Georg Placzek in his autobiography (1989, p. 90). According to T. Oka (2011)(pdf): Placzek (1934) introduced the currently used symbols of irreducible representations such as A (...
Francois Ziegler's user avatar
2 votes
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Earliest known usage of letter gamma "Γ" for reducible representation in group theory

Early examples are Burnside (1910, pp. 324-325; 1911, p. 271) where $\color{red}{\textrm{ir}}$reducible representations are called $\Gamma$, $\Gamma_1$, $\Gamma_2$, etc. (Earlier in (1901) he had ...
Francois Ziegler's user avatar
2 votes

What are the origins of the study of symmetry as a subject in itself?

As a side remark: I recommend warmly the book: "From Summetria to Symmetry: The Making of a Revolutionary Scientific Concept" by Hon\Goldstein, which deals with the emergence of the concept of ...
David's user avatar
  • 113
1 vote

Continuation on Galois’ lost memoir(s): was Poisson right in his review of Galois’ memoir?

There is already some pro-Poisson remarks in Peter Neumann’s “The writings of Evariste Galois”. One is by Neumann himself: With hindsight one may feel that this report was wrong. But I cannot think ...
anqian's user avatar
  • 31
1 vote

Exact quote (and source of) by John Conway regarding the action/origin of the Monster?

I found this statement in a short IAS article, In [Conway's] view, conformal field theory is too complicated to understand, and thus too complicated to be the only answer. However, seeing as ...
Carl Witthoft's user avatar
1 vote

Early discoveries combining groups and geometry?

The earliest applications of groups in geometry are dealing with continuous groups (Lie, Klein 1872). You seem to be talking about discrete groups. Their earliest application in a geometric subject ...
Alexandre Eremenko's user avatar

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