Geodesic
Infinite chains of successive normalizers in the general linear group
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 30-66 
A. H. Al-Hamad; Z. I. Borevich. Infinite chains of successive normalizers in the general linear group. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 30-66. http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a2/
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     author = {A. H. Al-Hamad and Z. I. Borevich},
     title = {Infinite chains of successive normalizers in the general linear group},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--66},
     year = {1994},
     volume = {211},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $K$ be a field of characteristics 0 or a field of characteristic 2 and of transcendence degree $\ge1$, and let $\mathrm{G=GL}(n,K)$ be the general linear group of degree $n\ge2$ over $K$. Further, let $1\le\rho\le\frac{n^2}4$. It is proved that in $\mathrm G$ there exist chains of subgroups $\{H_m\colon m\in\mathbb Z\}$, infinite in both directions, such that $H_m, $H_{m-1}$ coincides with the normalizer $\mathcal N_\mathrm G(H_m)$, and every quotient group $H_{m-1}/H_m$ is an elementary Abelian group of type $(2,2,\dots,2)$ and of rank $\rho$. Bibliography: 7 titles.