Geodesic
Generating sets of conjugate involutions of groups $PSL_{n}(9)$
Algebra i logika, Tome 62 (2023) no. 4, pp. 479-503

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

G. Malle, J. Saxl, and T. Weigel in [Geom. Ded., 49, No. 1, 85—116 (1994)] formulated the following problem: For every finite simple non-Abelian group $G$, find the minimum number $n_c(G)$ of generators of conjugate involutions whose product equals 1. (See also Question 14.69c in [Unsolved Problems in Group Theory. The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022); https://alglog.org/20tkt.pdf].) J. M. Ward [PhD Thesis, Queen Mary College, Univ. London (2009)] solved this problem for sporadic, alternating, and projective special linear groups $PSL_n(q)$ over a field of odd order $q$, except in the case $q=9$ for $n\geq4$ and also in the case $q\equiv3 ({\rm mod} 4)$ for $n=6$. Here we lift the restriction $q\neq9$ for dimensions $n\geq9$ and for the dimension $n=6$.
Keywords: skew-symmetric identity, finitely generated alternative algebra. 
@article{AL_2023_62_4_a2,
     author = {R. I. Gvozdev},
     title = {Generating sets of conjugate involutions of groups $PSL_{n}(9)$},
     journal = {Algebra i logika},
     pages = {479--503},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_4_a2/}
}
TY  - JOUR
AU  - R. I. Gvozdev
TI  - Generating sets of conjugate involutions of groups $PSL_{n}(9)$
JO  - Algebra i logika
PY  - 2023
SP  - 479
EP  - 503
VL  - 62
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2023_62_4_a2/
LA  - ru
ID  - AL_2023_62_4_a2
ER  - 
%0 Journal Article
%A R. I. Gvozdev
%T Generating sets of conjugate involutions of groups $PSL_{n}(9)$
%J Algebra i logika
%D 2023
%P 479-503
%V 62
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2023_62_4_a2/
%G ru
%F AL_2023_62_4_a2
R. I. Gvozdev. Generating sets of conjugate involutions of groups $PSL_{n}(9)$. Algebra i logika, Tome 62 (2023) no. 4, pp. 479-503. http://geodesic.mathdoc.fr/item/AL_2023_62_4_a2/