IMAGES OF WORD MAPS IN FINITE SIMPLE GROUPS
Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 465-469

Voir la notice de l'article provenant de la source Cambridge University Press

In response to questions by Kassabov, Nikolov and Shalev, we show that a given subset A of a finite simple group G is the image of some word map w : G × G → G if and only if (i) A contains the identity and (ii) A is invariant under Aut(G).
DOI : 10.1017/S0017089513000396
Mots-clés : 20D05, 20F10
LUBOTZKY, ALEXANDER. IMAGES OF WORD MAPS IN FINITE SIMPLE GROUPS. Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 465-469. doi: 10.1017/S0017089513000396
@article{10_1017_S0017089513000396,
     author = {LUBOTZKY, ALEXANDER},
     title = {IMAGES {OF} {WORD} {MAPS} {IN} {FINITE} {SIMPLE} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {465--469},
     year = {2014},
     volume = {56},
     number = {2},
     doi = {10.1017/S0017089513000396},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000396/}
}
TY  - JOUR
AU  - LUBOTZKY, ALEXANDER
TI  - IMAGES OF WORD MAPS IN FINITE SIMPLE GROUPS
JO  - Glasgow mathematical journal
PY  - 2014
SP  - 465
EP  - 469
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000396/
DO  - 10.1017/S0017089513000396
ID  - 10_1017_S0017089513000396
ER  - 
%0 Journal Article
%A LUBOTZKY, ALEXANDER
%T IMAGES OF WORD MAPS IN FINITE SIMPLE GROUPS
%J Glasgow mathematical journal
%D 2014
%P 465-469
%V 56
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000396/
%R 10.1017/S0017089513000396
%F 10_1017_S0017089513000396

[1] 1.Guralnick, R. M. and Kantor, W. M., Probabilistic generation of finite simple groups. Special issue in honor of Helmut Wielandt, J. Algebra 234 (2000), 743–792. Google Scholar

[2] 2.Hadad, U., On the shortest identity in finite simple groups of Lie type, J. Group Theory 14 (2011), 37–47. Google Scholar

[3] 3.Jambor, S., Liebeck, M. W. and O'Brien, E. A., Some word maps that are non-surjective on infinitely many finite simple groups, Bull. LMS (2013), doi: 101112/blms/bdt10. (arXiv:1205.1952). Google Scholar

[4] 4.Kantor, W. M. and Lubotzky, A., The probability of generating a finite classical group, Geom. Dedicata 36 (1990), 67–87. Google Scholar | DOI

[5] 5.Kassabov, M. and Nikolov, N., Words with few values in finite simple groups, preprint (arXiv:1112.5484). Q. J. Math. (2012), doi: 10.1093/qmath/has018. Google Scholar

[6] 6.Larsen, M., Shalev, A. and Tiep, P. H., The Waring problem for finite simple groups, Ann. Math. 174 (2011), 1885–1950. Google Scholar

[7] 7.Levy, M., Word maps with small image in simple groups, preprint (arXiv:1206.1206). Google Scholar

[8] 8.Levy, M., Images of word maps in almost simple groups and quasisimple groups, preprint (arXiv:1301.7188). Google Scholar

[9] 9.Liebeck, M. W., O'Brien, E. A., Shalev, A. and Tiep, P. H., The Ore conjecture, J. Eur. Math. Soc. 12 (2010), 939–1008. Google Scholar | DOI

[10] 10.Segal, D., Words: Notes on verbal width in groups, London Mathematical Society Lecture Note Series, 361 (Cambridge University Press, Cambridge, UK, 2009), xii+121 pp. Google Scholar

[11] 11.Spenko, S., On the image of a noncommutative polynomial, J. Algebra 377 (2013), 298–311. Google Scholar

[12] 12.Wilson, J. S., Finite index subgroups and verbal subgroups in profinite groups, Séminaire Bourbaki, vol. 2009/2010. Exposés 1012–1026. Astérisque No. 339 (2011), Exp. No. 1026, x, 387–408. Google Scholar

Cité par Sources :