Geodesic
Generating triples of involutions of groups of Lie type of rank two over finite fields
Algebra i logika, Tome 58 (2019) no. 1, pp. 84-107.

Voir la notice de l'article provenant de la source Math-Net.Ru

For finite simple groups $U_5(2^n)$, $n>1$, $U_4(q)$, and $S_4(q)$, where $q$ is a power of a prime $p > 2$, $q-1\ne0\pmod4$, and $q\ne 3$, we explicitly specify generating triples of involutions two of which commute. As a corollary, it is inferred that for the given simple groups, the minimum number of generating conjugate involutions, whose product equals $1$, is equal to $5$.
Keywords: group of Lie type, finite simple group, generating triples of involutions. 
@article{AL_2019_58_1_a5,
     author = {Ya. N. Nuzhin},
     title = {Generating triples of involutions of groups of {Lie} type of rank two over finite fields},
     journal = {Algebra i logika},
     pages = {84--107},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_1_a5/}
}
TY  - JOUR
AU  - Ya. N. Nuzhin
TI  - Generating triples of involutions of groups of Lie type of rank two over finite fields
JO  - Algebra i logika
PY  - 2019
SP  - 84
EP  - 107
VL  - 58
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2019_58_1_a5/
LA  - ru
ID  - AL_2019_58_1_a5
ER  - 
%0 Journal Article
%A Ya. N. Nuzhin
%T Generating triples of involutions of groups of Lie type of rank two over finite fields
%J Algebra i logika
%D 2019
%P 84-107
%V 58
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2019_58_1_a5/
%G ru
%F AL_2019_58_1_a5
Ya. N. Nuzhin. Generating triples of involutions of groups of Lie type of rank two over finite fields. Algebra i logika, Tome 58 (2019) no. 1, pp. 84-107. http://geodesic.mathdoc.fr/item/AL_2019_58_1_a5/

[1] Ya. N. Nuzhin, “Porozhdayuschie troiki involyutsii znakoperemennykh grupp”, Matem. zametki, 51:4 (1992), 91–95 | Zbl

[2] Ya. N. Nuzhin, “Porozhdayuschie troiki involyutsii grupp Shevalle nad konechnym polem kharakteristiki 2”, Algebra i logika, 29:2 (1990), 192–206 | Zbl

[3] Ya. N. Nuzhin, “Porozhdayuschie troiki involyutsii grupp lieva tipa nad konechnym polem nechetnoi kharakteristiki. I”, Algebra i logika, 36:1 (1997), 77–96 | Zbl

[4] Ya. N. Nuzhin, “Porozhdayuschie troiki involyutsii grupp lieva tipa nad konechnym polem nechetnoi kharakteristiki. II”, Algebra i logika, 36:4 (1997), 422–440 | Zbl

[5] V. D. Mazurov, “O porozhdenii sporadicheskikh prostykh grupp tremya involyutsiyami, dve iz kotorykh perestanovochny”, Sib. matem. zh., 44:1 (2003), 193–198 | Zbl

[6] J. N. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[7] Unsolved problems in group theory, The Kourovka notebook, 19, Sobolev Institute of Mathematics, Novosibirsk, 2018 http://www.math.nsc.ru/ãlglog/19tkt.pdf

[8] J. M. Ward, Generation of simple groups by conjugate involutions, PhD Thesis, Queen Mary college, Univ. London, 2009

[9] E. S. Rapaport, “Cayley color groups and Hamilton lines”, Scripta Math., 24 (1959), 51–58 | MR | Zbl

[10] I. Pak, R. Radoicic, “Hamiltonian paths in Cayley graphs”, Discrete Math., 309:17 (2009), 5501–5508 | MR | Zbl

[11] G. A. Jones, Automorphism groups of edge-transitive maps, arXiv: 1605.09461 [math.CO] | MR

[12] M. Macaj, “On minimal kaleidoscopic regular maps with trinity symmetry”, The seventh workshop Graph Embeddings and Maps on Surfaces, Abstracts (Podbanske, Slovakia, 30 July–4 August, 2017), 2017

[13] R. W. Carter, Simple groups of Lie type, Pure and Appl. Math., 28, John Wiley Sons, a Wiley Intersci. Publ., London a.o., 1972 | MR

[14] L. E. Dickson, Linear groups with an exposition of the Galois field theory, B.G. Teubner, Leipzig, 1901

[15] D. Gorenstein, Finite groups, Harper's Ser. Modern Math., Harper Row Publ., New York a.o., 1968 | MR | Zbl

[16] Ya. H. Nuzhin, “Porozhdayuschie mnozhestva elementov grupp Shevalle nad konechnym polem”, Algebra i logika, 28:6 (1989), 670–686 | Zbl

[17] V. M. Levchuk, “Zamechanie k teoreme L. Diksona”, Algebra i logika, 22:4 (1983), 421–434 | Zbl

[18] Ya. N. Nuzhin, “O gruppakh, zaklyuchennykh mezhdu gruppami lieva tipa nad razlichnymi polyami”, Algebra i logika, 22:5 (1983), 526–541 | Zbl