Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 869-876
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V. V. Kabanov; A. I. Starostin. Finite groups in which a Sylow two-subgroup of the centralizer of some involution is of order 16. Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 869-876. http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a8/
@article{MZM_1975_18_6_a8,
author = {V. V. Kabanov and A. I. Starostin},
title = {Finite groups in which {a~Sylow} two-subgroup of the centralizer of some involution is of order 16},
journal = {Matemati\v{c}eskie zametki},
pages = {869--876},
year = {1975},
volume = {18},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a8/}
}
TY - JOUR
AU - V. V. Kabanov
AU - A. I. Starostin
TI - Finite groups in which a Sylow two-subgroup of the centralizer of some involution is of order 16
JO - Matematičeskie zametki
PY - 1975
SP - 869
EP - 876
VL - 18
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a8/
LA - ru
ID - MZM_1975_18_6_a8
ER -
%0 Journal Article
%A V. V. Kabanov
%A A. I. Starostin
%T Finite groups in which a Sylow two-subgroup of the centralizer of some involution is of order 16
%J Matematičeskie zametki
%D 1975
%P 869-876
%V 18
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a8/
%G ru
%F MZM_1975_18_6_a8
It is proved that the sectional two-rank of a finite group $G$ having no subgroup of index two is at most four if a Sylow two-subgroup of the centralizer of some involution of $G$ is of order 16. This implies the following assertion: If $G$ is a finite simple group whose order is divisible by $2^5$ and the order of the centralizer of some involution of $G$ is not divisible by $2^5$, then $G$ is isomorphic to the Mathieu group $M_{12}$ or the Hall–Janko group $J_2$.
