Geodesic
On $3$-generated $6$-transposition groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 540-554 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study $6$-transposition groups, i.e. groups generated by a normal set of involutions $D$, such that the order of the product of any two elements from $D$ does not exceed $6$. We classify most of the groups generated by $3$ elements from $D$, two of which commute, and prove they are finite.
Mots-clés : $6$-transposition group. 
@article{SEMR_2024_21_2_a1,
     author = {V. A. Afanasev and A. S. Mamontov},
     title = {On $3$-generated $6$-transposition groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {540--554},
     year = {2024},
     volume = {21},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a1/}
}
TY  - JOUR
AU  - V. A. Afanasev
AU  - A. S. Mamontov
TI  - On $3$-generated $6$-transposition groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 540
EP  - 554
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a1/
LA  - en
ID  - SEMR_2024_21_2_a1
ER  - 
%0 Journal Article
%A V. A. Afanasev
%A A. S. Mamontov
%T On $3$-generated $6$-transposition groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 540-554
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a1/
%G en
%F SEMR_2024_21_2_a1
V. A. Afanasev; A. S. Mamontov. On $3$-generated $6$-transposition groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 540-554. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a1/

[1] M. Aschbacher, 3-transposition groups, Cambridge University Press, Cambridge, 1997 | MR | Zbl

[2] H. Cuypers, J.I. Hall, “The 3-transposition groups with trivial center”, J. Algebra, 178:1 (1995), 149–193 | DOI | MR | Zbl

[3] S. Decelle, Majorana representations and the Coxeter groups $G^{(m,n,p)}$, Ph.D. thesis, Imperial College, London, 2014

[4] L. Di Martino, M.A. Pellegrini, A.E. Zalesski, “On generators and representations of the sporadic simple groups”, Commun. Algebra, 42:2 (2014), 880–908 | DOI | MR | Zbl

[5] B. Fischer, “Finite groups generated by 3-transpositions. I”, Invent. Math., 13 (1971), 232–246 | DOI | MR | Zbl

[6] C. Franchi, A.A. Ivanov, M. Mainardis, “Saturated Majorana representations of $A_{12}$”, Trans. AMS, 375:8 (2022), 5753–5801 | DOI | MR | Zbl

[7] GAP – Groups, Algorithms, and Programming, Version 4.12.1, , 2022 https://www.gap-system.org

[8] J.L. Gross, T.W. Tucker, Topological graph theory, Wiley Sons, New York etc., 1987 | MR | Zbl

[9] J.I. Hall, “Generating finite 3-transposition groups”, J. Algebra, 607 (2022), 338–371 | DOI | MR | Zbl

[10] J.I. Hall, L.H. Soicher, “Presentations of some 3-transposition groups”, Commun. Algebra, 23:7 (1995), 2517–2559 | DOI | MR | Zbl

[11] S. Khasraw, J. McInroy, S. Shpectorov, “Enumerating 3-generated axial algebras of Monster type”, J. Pure Appl. Algebra, 226:2 (2022), 106816 | DOI | MR | Zbl

[12] A. Mamontov, A. Staroletov, M. Whybrow, “Minimal 3-generated Majorana algebras”, J. Algebra, 524 (2019), 367–394 | DOI | MR | Zbl