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Topic · Discrete Mathematics and Combinatorics

Finite Group Theory Research

Finite Group Theory Research is a research topic within Discrete Mathematics and Combinatorics. Science Explorer counts 24k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the study of finite groups, their representations, and associated graphs such as Cayley graphs and distance-regular graphs. It also explores topics like character degrees, fusion systems, and linear transformations in the context of finite group theory.

  • Finite Groups
  • Graphs
  • Character Degrees
  • Cayley Graphs
  • Association Schemes
  • Linear Transformations
  • Distance-Regular Graphs
  • Fusion Systems
  • Tridiagonal Pairs
  • Representation Theory
Research works
24k
fractional, since 1950
In the world top 10%
2.4k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+15%
the tick is no change
Largest producer
China
29% of the 10 largest, 2022-now
Finite Group Theory Research

Which countries lead Finite Group Theory Research research?

By volume, China and the United States publish the most (644 and 366 works in 2022-now).

By volume, 2022-now

  1. 1 China 644 works
  2. 2 United States 366 works
  3. 3 India 267 works
  4. 4 Russia 186 works
  5. 5 Germany 149 works
  6. 6 Italy 149 works
  7. 7 United Kingdom 142 works
  8. 8 Japan 109 works
  9. 9 France 100 works
  10. 10 Iran 98 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 29.1%United States: 16.6%India: 12.1%Russia: 8.4%6 others listed: 33.8%29%largest
China644 · 29.1%United States366 · 16.6%India267 · 12.1%Russia186 · 8.4%6 others listed748 · 33.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Finite Group Theory Research research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Finite Group Theory Research research, followed by Centre National de la Recherche Scientifique and Francisk Skorina Gomel State University.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 68 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 48 works
  3. 3 Francisk Skorina Gomel State UniversityBelarus 28 works
  4. 4 Ghent UniversityBelgium 23 works
  5. 5 University of PrimorskaSlovenia 21 works
  6. 6 Universidade de BrasíliaBrazil 20 works
  7. 7 Universitat de ValènciaSpain 20 works
  8. 8 University of Naples Federico IIItaly 20 works
  9. 9 Southern University of Science and TechnologyChina 16 works
  10. 10 Beijing Jiaotong UniversityChina 16 works

Who are the leading researchers in Finite Group Theory Research?

The most-cited researchers publishing on Finite Group Theory Research include Eric S. Lander, Stephen M. Smith and Michael Weller.

  1. 1 Eric S. Lander United States 524k citations
  2. 2 Stephen M. Smith United Kingdom 214k citations
  3. 3 Michael Weller Switzerland 172k citations
  4. 4 Jin Li China 132k citations
  5. 5 Hywel C Williams United Kingdom 126k citations
  6. 6 Hao Chen China 118k citations
  7. 7 John F. Thompson Australia 118k citations
  8. 8 Peter C. Austin Canada 113k citations
  9. 9 John A. Todd United Kingdom 107k citations
  10. 10 Jinde Cao China 104k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Finite Group Theory Research?

The most cited paper in Finite Group Theory Research is "Partial differential equations of parabolic type" (John S. Maybee, 1965), with 3,305 citations. Next come "Compact matrix pseudogroups" (1,700) and "SIMPLE GROUPS OF LIE TYPE" (1,471).

Most cited papers
#PaperReleasedCitations
1 Partial differential equations of parabolic type John S. Maybee · Journal of the Franklin Institute Jun 1965 3,305
2 Compact matrix pseudogroups Stanisław Lech Woronowicz · Communications in Mathematical Physics Open access Dec 1987 1,700
3 SIMPLE GROUPS OF LIE TYPE Ian G. MacDonald · Bulletin of the London Mathematical Society Mar 1975 1,471
4 Groupes réductifs sur un corps local : I. Données radicielles valuées François Bruhat, Jacques Tits · Publications mathématiques de l IHÉS 7 Dec 1972 1,043
5 Ramanujan graphs Alexander Lubotzky, Ralph S. Phillips, Peter Sarnak · COMBINATORICA Sep 1988 1,015
All 100 most cited papers, with filters and sorting

Where is Finite Group Theory Research research done?

The largest centres of Finite Group Theory Research research in 2022-now are Moscow (Russia), Beijing (China), Novosibirsk (Russia) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Homyel, Koper and Novosibirsk.

Largest cities, 2022-now

  1. 1 MoscowRussia 77 works
  2. 2 BeijingChina 73 works
  3. 3 NovosibirskRussia 45 works
  4. 4 ShanghaiChina 38 works
  5. 5 TokyoJapan 37 works
  6. 6 GuangzhouChina 35 works
  7. 7 TehranIran 33 works
  8. 8 ParisFrance 31 works
  9. 9 HomyelBelarus 29 works
  10. 10 LondonUnited Kingdom 27 works

Where it is the local speciality

  1. HomyelBY · 29.4 works172×
  2. KoperSI · 20.8 works107×
  3. NovosibirskRU · 44.9 works12×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Finite Group Theory Research than the world average.

See Finite Group Theory Research on the map

Where is the best place to study Finite Group Theory Research?

Among universities, judged by research, Ghent University, University of Primorska and Universitat de València score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 13.96%fractional works in this field (log) →share of work in the world top 10% →Universitat de Valèn…Ghent UniversityUniversity of Primor…Francisk Skorina Gom…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Ghent UniversityBelgium 62.38.3%10.5×23 +46.5%
2University of PrimorskaSlovenia 60.47.9%130.7×21 +45.6%
3Universitat de ValènciaSpain 59.110.5%12.8×20 +29.4%
4Francisk Skorina Gomel State UniversityBelarus 56.51.4%589.8×28 -2.0%
5University of Campania "Luigi Vanvitelli"Italy 56.537.8%13.3×8 -7.0%
6Southern University of Science and TechnologyChina 55.610.4%10.5×16 +205.7%
7Vrije Universiteit BrusselBelgium 55.123.8%10.1×8 +27.3%
8Nankai UniversityChina 51.219.4%6.2×12 +74.6%
9University of Milano-BicoccaItaly 50.77.8%15.4×12 +32.4%
10University of Naples Federico IIItaly 50.512.3%9.7×20 -6.6%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Finite Group Theory Research, country by country

Is Finite Group Theory Research research growing?

Output in 2022-2025 was 15% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Finite Group Theory Research.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Finite Group Theory Research as a percentage of every work published that year, 0.014% in 2024.

still counting0.025%0.050%0.075%Finite Group Theory Research0.012% in 202519801990200020102020

Fractional works of Finite Group Theory Research over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Finite Group Theory Research9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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