We prove that, confined that G > H > P and P is a proper p-subgroup of H, if H ∩~gH ≤ P for any g ∈ G-H, then the operator of the restriction to RH of RG-modules induces a triangulated equivalence from StmodP...We prove that, confined that G > H > P and P is a proper p-subgroup of H, if H ∩~gH ≤ P for any g ∈ G-H, then the operator of the restriction to RH of RG-modules induces a triangulated equivalence from StmodP(RG) to StmodP(RH); if the normal subgroup H controls the fusion of p-subgroups of G, the restriction functor is a faithful triangulated functor; if P is strongly closed in H respect to G, the same functor is also a faithful triangulated functor.展开更多
In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give ...In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.展开更多
基金Supported by the National Natural Science Foundation of China(10826057)
文摘We prove that, confined that G > H > P and P is a proper p-subgroup of H, if H ∩~gH ≤ P for any g ∈ G-H, then the operator of the restriction to RH of RG-modules induces a triangulated equivalence from StmodP(RG) to StmodP(RH); if the normal subgroup H controls the fusion of p-subgroups of G, the restriction functor is a faithful triangulated functor; if P is strongly closed in H respect to G, the same functor is also a faithful triangulated functor.
文摘In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.
