Geodesic
Groups with an almost regular involution
Algebra i logika, Tome 46 (2007) no. 3, pp. 360-368

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

An involution j of a group $G$ is said to be almost perfect in $G$ if any two involutions in $j^G$ whose product has infinite order are conjugated by a suitable involution in $j^G$. Let $G$ contain an almost perfect involution $j$ and $|C_G(j)|\infty$. Then the following statements hold: 1) $[j,G]$ is contained in an $FC$-radical of $G$, and $|G:[j,G]|\leqslant|C_G(j)|$; 2) the commutant of an $FC$-radical of $G$ is finite; 3) $FC(G)$ contains a normal nilpotent class 2 subgroup of finite index in $G$.
Mots-clés : group
Keywords: almost regular involution, almost perfect involution. 
@article{AL_2007_46_3_a4,
     author = {A. I. Sozutov},
     title = {Groups with an almost regular involution},
     journal = {Algebra i logika},
     pages = {360--368},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_3_a4/}
}
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A. I. Sozutov. Groups with an almost regular involution. Algebra i logika, Tome 46 (2007) no. 3, pp. 360-368. http://geodesic.mathdoc.fr/item/AL_2007_46_3_a4/