On the generation of finite groups by classes of involutions
Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 243-253
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $D$ be an invariant subset of involutions of the finite group $G$. $D$ satisfies the condition of coherence, if for any two distinct commuting involutions of $D$ their product also belongs to $D$. $D$ satisfies the condition of separability if the product of any two involutions of is a 2-element or a $2'$-element.
In this paper it is proved that if the finite group $G$ is generated by an invariant subset of involutions $D$ satisfying the coherence and separability conditions, and if $D\cap O_2(G)=\varnothing$, then either $G$ has a Sylow 2-subgroup of order 2, or $Z(G)$ has odd order, $G=G'$, and the factor group $G/Z(G)$ is isomorphic to one of the following simple groups: $L_2(p)$, $p$ a Fermat or a Mersenne prime number, $L_2(q)$, $Sz(q)$, $U_3(q)$, $L_3(q)$, $G_2(q)$ ($G_2(q)'$ respectively), $^3D_4(q)$, $q$ even, $A_6$ or $J_2$.
Bibliography: 25 titles.
@article{SM_1981_39_2_a5,
author = {A. A. Makhnev},
title = {On the generation of finite groups by classes of involutions},
journal = {Sbornik. Mathematics},
pages = {243--253},
publisher = {mathdoc},
volume = {39},
number = {2},
year = {1981},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1981_39_2_a5/}
}
A. A. Makhnev. On the generation of finite groups by classes of involutions. Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 243-253. http://geodesic.mathdoc.fr/item/SM_1981_39_2_a5/