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

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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/}
}
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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/