Geodesic
Finite simple groups with Sylow 2-subgroups of order~$2^7$
Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 709-723.

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

The following theorem is proved in the paper. If a Sylow 2-subgroup $T$ of a finite simple group is of order $2^7$ , then either the nilpotency class of $T$ is not greater than 2 or the sectional 2-rank of $T$ does not exceed 4. This theorem and known classification results lead to a list of all finite simple groups with Sylow 2-subgroups of order $\leqslant2^7$. Bibliography: 22 titles. 
@article{IM2_1977_11_4_a1,
     author = {A. S. Kondrat'ev},
     title = {Finite simple groups with {Sylow} 2-subgroups of order~$2^7$},
     journal = {Izvestiya. Mathematics },
     pages = {709--723},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a1/}
}
TY  - JOUR
AU  - A. S. Kondrat'ev
TI  - Finite simple groups with Sylow 2-subgroups of order~$2^7$
JO  - Izvestiya. Mathematics 
PY  - 1977
SP  - 709
EP  - 723
VL  - 11
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a1/
LA  - en
ID  - IM2_1977_11_4_a1
ER  - 
%0 Journal Article
%A A. S. Kondrat'ev
%T Finite simple groups with Sylow 2-subgroups of order~$2^7$
%J Izvestiya. Mathematics 
%D 1977
%P 709-723
%V 11
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a1/
%G en
%F IM2_1977_11_4_a1
A. S. Kondrat'ev. Finite simple groups with Sylow 2-subgroups of order~$2^7$. Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 709-723. http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a1/

[1] Kondratev A. S., “Konechnye prostye gruppy, silovskie 2-podgruppy kotorykh imeyut tsiklicheskii kommutant”, Sib. matem. zh., 17:1 (1976), 85–90 | MR

[2] Kondratev A. S., “Konechnye prostye gruppy, silovskaya 2-podgruppa kotorykh est rasshirenie abelevoi gruppy posredstvom gruppy ranga 1”, Algebra i logika, 14:3 (1975), 288–303 | MR

[3] Sitnikov V. M., “O konechnykh gruppakh s samotsentralizuyuscheisya podgruppoi poryadka 8”, Vsesoyuznyi algebraicheskii simpozium, tezisy dokladov, chast pervaya, Gomel, 1975, 63

[4] Ustyuzhaninov A. D., “O konechnykh $p$-gruppakh, kommutant kazhdoi sobstvennoi podgruppy kotorykh metatsiklicheskii”, Sib. matem. zh., 12:4 (1971), 844–854

[5] Bechtel H., “Frattini subgroups and $Phi$-central groups”, Pacif. J. Math., 18:1 (1966), 15–23 | MR | Zbl

[6] Chabot P., “Groups whose Sylow 2-groups have cyclic commutator groups”, J. Algebra, 19:1 (1971), 21–30 | DOI | MR | Zbl

[7] Gilman R., Gorenstein D., “Finite groups with Sylow 2-subgroups of class two, I. II”, Trans. Amer. Math. Soc., 207:480 (1975), 1–101, 103–126 | DOI | MR | Zbl

[8] Glauberman G., “Central elements in core-free groups”, J. Algebra, 4:3 (1966), 403–420 | DOI | MR | Zbl

[9] Glauberman G., “Global and local properties of finite groups”, Finite simple groups, eds. M. B. Powell, G. Higman, Academic Press, London, New York, 1971 | MR

[10] Goldschmidt D. M., “2-Fusion in finite groups”, Ann. Math., 99:1 (1974), 70–117 | DOI | MR | Zbl

[11] Gorenstein D., Finite groups, Harper and Row, New York, Evanston, London, 1968 | MR | Zbl

[12] Gorenstein D., Harada K., “Finite groups whose 2-subgroups are generated by at most 4 elements”, Mem. Amer. Math. Soc., 147 (1974), 1–464 | MR

[13] Harada K., “Finite simple groups with short chains of subgroups”, J. Math. Soc. Japan, 20:4 (1968), 655–672 | MR | Zbl

[14] Huppert B., Endliche Gruppen, I, Springer-Verlag, Berlin, 1967 | MR | Zbl

[15] Landrock P., “Finite groups with a quasisimple component of type $PSU(3,2^n)$ on elementary abelian form”, Ill. J. Math., 19:2 (1975), 198–230 | MR | Zbl

[16] Walter J. H., “The characterization of finite groups with abelian Sylow 2-subgroups”, Ann. Math., 89:3 (1969), 405–514 | DOI | MR | Zbl

[17] Wielandt H., “$p$-Sylowgruppen und $p$-Faktorgruppen”, J. Reine Angew. Math., 182 (1940), 180–193 | MR | Zbl

[18] Janko Z., “Finite groups with invariant fourth maximal subgroups”, Math. Z., 82:1 (1963), 82–89 | DOI | MR | Zbl

[19] Janko Z., “Finite simple groups with short chains of subgroups”, Math. Z., 84:4 (1964), 428–437 | DOI | MR | Zbl

[20] Čepulič V., “On finite groups of length 8”, Ill. J. Math, 18:3 (1974), 389–417

[21] Baumann B., “Endliche nichtauflösbare Gruppen mit einer nilpotenten maximalen Untergruppe”, J. Algebra, 38:1 (1976), 119–135 | DOI | MR | Zbl

[22] Hall M. Jr., “Simple groups of order less than one million”, J. Algebra, 20:1 (1972), 98–102 | DOI | MR | Zbl