Garlands containing the general linear group over an intermediate field

Let K/k be a finite extension of fields with an intermediate subfield L, and let H = GL_L(K) be the general linear group of all L-linear invertible mappings of the vector space of the field K over L. It is proved that the subgroups lying between GL_K(K)^H and the normalizer of H in G, where G = GL_k(K), form a garland. Bibliography: 4 titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 34–41.