Talk:Group theory

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Proposed merger with "Examples of Groups"

I believe including examples of groups would unnecessarily clutter the page. The main page should be reserved for definitions and properties of groups in general. Examples of groups is a useful page which many people who don't understand what groups are will find useful, however it does not belong on this page IMO. 2002:80ED:AA45:0:0:0:80ED:AA45 (talk) 16:45, 30 September 2016 (UTC)[reply]

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History section placement

Why is History so far down the page? It seems to me this should immediately follow the lead.—Anita5192 (talk) 23:29, 25 April 2020 (UTC)[reply]

Resolved

Lbertolotti (talk) 00:30, 10 June 2022 (UTC)[reply]

"Glossary of group theory" listed at Redirects for discussion

A discussion is taking place to address the redirect Glossary of group theory. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 June 10#Glossary of group theory until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Tea2min (talk) 10:06, 10 June 2020 (UTC)[reply]

Top image

Can the Rubik's cube image be replaced for example by Cayley diagram like the one on the right?

I think it illustrates things more clearly. Though the group actions and starting element probably need to be described more clearly. — Preceding unsigned comment added by Dewitt Sciullo (talk • contribs) 20:17, 16 August 2020 (UTC)[reply]

Relationship with Set Theory

Group Theory, as a subset of set theory, needs to be understood as being part of a broader area of Math. This article should have links to ZFT and the older set theory of Frege. I also think Cantor and the Continuum Hypothesis need to be mentioned because Group Theory has become quite relevant to that area and vice versa. CessnaMan1989 (talk) 18:11, 5 October 2021 (UTC)[reply]

Group theory is not a subset of set theory. Set theory can be used as a foundation for much of mathematics, including group theory, but there are other foundational theories that work equally well in its place. —David Eppstein (talk) 18:49, 5 October 2021 (UTC)[reply]

Applications to Computer Networking

Should applications of Group Theory to Computer Networking be specifically discussed? CessnaMan1989 (talk) 00:53, 5 November 2021 (UTC)[reply]

That is far too vague a question to have a good answer. Which applications, and which published reliable sources do you have in mind describing those applications? —David Eppstein (talk) 01:22, 5 November 2021 (UTC)[reply]

I was thinking of applications of permutation groups to data storage. For sources, I have commenting in GitHub code and software readme's. I also have read a few patent applications describing such use. For example, (US7240236, Fixed content distributed data storage using permutation ring encoding, Shaun Cutts and Andres Rodriguez). CessnaMan1989 (talk) 02:45, 5 November 2021 (UTC)[reply]

See Wikipedia's requirements on reliable sources. Textbooks or peer-reviewed survey papers would count as reliable secondary sources, in this sense. Research papers in peer-reviewed conferences and journals are also reliable, but primary, and might also be usable. Comments in Github code and patent applications would definitely not. —David Eppstein (talk) 06:10, 5 November 2021 (UTC)[reply]

What about granted patents? I see mixed and seemingly conflicted guidelines about citing patents. CessnaMan1989 (talk) 14:50, 5 November 2021 (UTC)[reply]

I think in this case a patent is likely to require far too much reader interpretation to connect it to the topic. The one you linked above, for instance, talks about "permutation rings". I don't know what a permutation ring might be, and even if it describes a significant and encyclopedia-worthy contribution (also not clear) it's not at all clear that it belongs in a general article about group theory rather than in an article involving one of cycle (graph theory), ring (mathematics), permutation group, permutation, or something else, depending on what "permutation ring" turns out to mean. —David Eppstein (talk) 20:05, 6 November 2021 (UTC)[reply]

Applications in the Social Sciences

There isn't any information about applications of Group theory in the Social Sciences. The Wikipedia page for Mathematical Sociology ^[1] mentions applications of Group Theory in Sociology literature, e.g in "White, Harrison C. 1963. An Anatomy of Kinship. Prentice-Hall", as well as "Wasserman, S., & Faust, K.. Social Network Analysis: Methods and Applications. New York and Cambridge, ENG: Cambridge University Press". I'm also wondering what other applications could exist, separate from those mentioned. Tamedu quaternion (talk) 08:22, 8 January 2022 (UTC)[reply]

What Social Sciences call a group is not what mathematics calls a group. In mathematics a group is defined at Group (mathematics) as a set equipped with an operation that combines any two elements to form a third element, while being associative as well as having an identity element and inverse elements. A "social group" is a set of persons, but there is no combination of an arbitrary pair of elements to form a third with the associative, identity and inverse properties. In mathematics a social group is just a set, and not a mathematical group. So there is no reason to include it in this article. Dirac66 (talk) 00:43, 14 January 2022 (UTC)[reply]

Look at the reference. It really is about the abstract algebra kind of group theory, applied to social science, something to do with classifying possible kinship relations. If you want another reference whose title makes the connection more obvious, see Reid, Russell M. (April 1967), "Marriage Systems and Algebraic Group Theory: A Critique of White's An Anatomy of Kinship", American Anthropologist, 69 (2), Wiley: 171–178, doi:10.1525/aa.1967.69.2.02a00040, JSTOR 669432. Whether it is a significant enough application to mention here is a different question. —David Eppstein (talk) 00:49, 14 January 2022 (UTC)[reply]

References

^ https://en.wikipedia.org/wiki/Mathematical_sociology

Abelian groups

Abelian groups are a main class of groups. They have their own structure theory. They are important throughout mathematics. They should be in the list of main examples. Zaslav (talk) 19:48, 6 August 2022 (UTC)[reply]

We do now have a separate article Abelian group. Also the term is mentioned once in this article, in the first line of the section Applications of group theory. But I agree that there should be some more information in this article, starting with the definition of an Abelian group. Dirac66 (talk) 21:26, 6 August 2022 (UTC)[reply]

[1] ttps://en.wikipedia.org/wiki/Mathematical_sociology

[1]