Geodesic
An evaluation of the Ph. Hall function on rank 1 groups of Lie type
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 2, pp. 50-56 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In 1936 Ph. Hall introduced the generalized $n$-th Eulerian function on finite groups and the associated function that is called the $n$-th Hall function. The values of the latter are estimated in the article for three of the four series of Lie type groups of rank 1. When $n=2$, these evaluations confirm the Wiegold conjecture for the groups. 
@article{VMJ_2012_14_2_a5,
     author = {Yu. Yu. Ushakov},
     title = {An evaluation of the {Ph.~Hall} function on rank~1 groups of {Lie} type},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {50--56},
     year = {2012},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_2_a5/}
}
TY  - JOUR
AU  - Yu. Yu. Ushakov
TI  - An evaluation of the Ph. Hall function on rank 1 groups of Lie type
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2012
SP  - 50
EP  - 56
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2012_14_2_a5/
LA  - ru
ID  - VMJ_2012_14_2_a5
ER  - 
%0 Journal Article
%A Yu. Yu. Ushakov
%T An evaluation of the Ph. Hall function on rank 1 groups of Lie type
%J Vladikavkazskij matematičeskij žurnal
%D 2012
%P 50-56
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2012_14_2_a5/
%G ru
%F VMJ_2012_14_2_a5
Yu. Yu. Ushakov. An evaluation of the Ph. Hall function on rank 1 groups of Lie type. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 2, pp. 50-56. http://geodesic.mathdoc.fr/item/VMJ_2012_14_2_a5/

[1] Hall Ph., “The Eulerian functions of a group”, Quart. J. Math., 7 (1936), 134–151 | DOI | Zbl

[2] Kourovskaya tetrad. Nereshennye voprosy teorii grupp, Izd. 17-e, dopolnennoe, IM SO RAN, Novosibirsk, 2010, 219 pp.

[3] Suchkov N. M., Prikhodko D. M., “O chisle par porozhdayuschikh grupp $L_2(2^m )$ i $Sz(2^{2k+1})$”, Sib. mat. zhurn., 42:5 (2001), 1162–1167 | MR | Zbl

[4] Erfanian A., Rezaei R., “On the growth sequence of $PSp(2m,q)$”, Intern. J. Algebra, 1:2 (2007), 51–62 | MR | Zbl

[5] Erfanian A., “A note on growth sequences of alternating groups”, Arch. Math., 78:4 (2002), 257–262 | DOI | MR | Zbl

[6] Erfanian A., “A note on growth sequences of $PSL(m,q)$”, Southeast Asian Bull. Math., 29:4 (2005), 697–713 | MR | Zbl

[7] Levchuk D. V., “Funktsii F. Kholla na gruppakh lieva tipa ranga 1”, Vladikavk. mat. zhurn., 10:1 (2008), 37–39 | MR

[8] Ushakov Yu. Yu., “Otsenka vtoroi funktsii Eilera na gruppakh lieva tipa ranga 1”, Tr. konf. “Algebra, logika i prilozheniya”, SFU, Krasnoyarsk, 2010, 101–102

[9] Prikhodko D. M., “O chisle par porozhdayuschikh elementov nekotorykh grupp $L_2(q)$”, Materialy 34-oi nauch. stud. konf., KrasGU, Krasnoyarsk, 2001, 91–102

[10] Erfanian A., “Growth Sequence of Free Product of Alternating Groups”, Int. J. Contemp. Math. Sc., 2:14 (2007), 685–691 | MR | Zbl

[11] Dickson L. E., Linear groups, Leipzig, 1901

[12] Levchuk V. M., Nuzhin Ya. N., “O stroenii grupp Li”, Algebra i logika, 24:1 (1985), 26–41 | MR | Zbl

[13] Suzuki M., “On a class of doubly transitive groups”, Ann. Math., 75:1 (1962), 105–145 | DOI | MR | Zbl

[14] Carter R. W., Simple Groups of Lie Type, Wiley and sons, London, 1972, 346 pp. | MR | Zbl

[15] http://www.gap-system.org