#group-theory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #group-theory, aggregated by home.social.
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#Mathematics #GroupTheory #Algebra #TheoreticalComputerScience
In my study (a while ago) I learned about Σ Algebras (theoretical computer science).
Then later, I learnt in math there are σ Algebras, which seems sort of the same thing.
Today I'm curious about group theory, and groups are also sort of the same thing.Can anyone tell me what's the difference? Between Σ Algebras, σ Algebras, and groups?
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Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.
\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)
\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.
\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]
The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.
The riff and rote for 2026 are shown in the next two Figures.
Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.pngRote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.pngReference —
Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotescc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes -
A section of a group G is a quotient of a subgroup, viz. K normal in H subgroup of G, the section is H/K.
Does anyone know if there is a more-or-less standard terminology not just for the section-up-to-isomorphism-of-the-group-H/K, but for the "instantiated" or maybe "concrete" section, e.g. the pair (K,H)?
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algebra final tmrw 😤 watch me cook
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Quanta Magazine really has nicely in-depth yet approachable writing on #mathematics, in this case an introduction to Lie groups #GroupTheory https://www.quantamagazine.org/what-are-lie-groups-20251203/
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Some time ago for practicing #haskell I implemented a well know algorithm for combining multiplets https://github.com/mdrslmr/MultipletCombiner . This algorithm from #grouptheory is used in #particlephysics and other #physics topics. The code is probably pretty useless since the results are anyway textbook standards. But I found it was a nice exercise. I'm sure the code can be improved a lot easily.
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Why are normal subgroups called "normal?" Most subgroups are not normal, which seemingly makes the name incorrect.
But in an Abelian group, all subgroups are normal. Abelian groups were the first groups to be studied by white European men, and they are the easiest for humans to work with.
Therefore, normal subgroups are called normal because they are the subgroups which pose the least challenge to the incumbent power structures.
#GroupTheory #NormalSubgroup -
Drafted a 3rd inquiry activity for D3 and D4 play with flips and rotations.
I am hoping it's not to dry. I'll read through it again tomorrow.
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#DocMadhattan: The Abel Prize 2025: Masaki Kashiwara
https://docmadhattan.hashnode.dev/the-abel-prize-2025-masaki-kashiwara
Masaki Kashiwara wins the 2025 Abel Prize for groundbreaking work in algebraic analysis, D-modules theory, and crystal bases in representation theory
#mathematics #physics #AbelPrize #MasakiKashiwara #grouptheory #quantumgroups
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Me: If you're a student in my class you will do group presentations, meaning that you will organize into a subset of the class, stand in front of the room, and talk about math to the rest of the class.
Also me: Let's talk about group presentations, a completely abstract algebraic concept that have absolutely nothing to do with standing in front of the room talking about your work.
Also also me: Okay, time for group presentations about group presentations.
#Algebra #ITeachMath #GroupTheory #GroupPresentation -
New 📚 Release! Introduction to Group Theory: An Activity-Based Approach by Joe Fox #books #ebooks #math #grouptheory
This book is an introduction to group theory suitable for an introductory course in abstract algebra. Much of the content is delegated to a series of activities that are meant to be worked through by the students with the help of the instructor.
Find it on Leanpub!
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Riffs and Rotes • Happy New Year 2025
• https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)
\( \text{Then} ~ 2025
= 81 \cdot 25
= 3^4 5^2 \)\( = {p_2}^4 {p_3}^2
= {p_2}^{{p_1}^{p_1}} {p_3}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.
\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]
The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.
Riff 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.pngRote 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.pngReference —
Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes -
A shop called "Wreath Products" that sells mathematical puzzle toys, mobiles (like for baby cribs or art)...and, sure, also decorative wreaths.
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Sat Dec 7, 2024 on zoom & in-person
Session in memory of Richard Parker at the annual Nikolaus conference at Aachen (on group & representation theory). Main speakers:
Gerhard Hiß
Gabriele Nebe
Colva Roney-Dougal -
This is honestly so cool. I love how kids toys and games can be the source of surprisingly complicated #math. In this case, using #groupTheory and #graphTheory to show how you can generate all possible configurations of a Rubik's cube without any repeats
https://bruce.cubing.net/ham333/rubikhamiltonexplanation.html
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This textbook has heavy “demon summoning” vibes to it 😅
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[New Blog Post] Coset Enumeration using Equality Saturation https://www.philipzucker.com/coset_enum_egraph/ #egraph #grouptheory #algebra
