Certain finite groups as automorphism groups of forms of higher degree
نویسندگان
چکیده
منابع مشابه
The Automorphism Group of Certain Higher Degree Forms
We consider symmetric indecomposable d-linear (d > 2) spaces of dimension n over an algebraically closed field k of characteristic 0, whose center (the analog of the space of symmetric matrices of a bilinear form) is cyclic, as introduced by Reichstein [R]. The automorphism group of these spaces is determined through the action on the center and through the determination of the Lie algebra. Fur...
متن کاملON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...
متن کامل0 M ar 2 00 7 AUTOMORPHISM GROUPS OF HIGHER DEGREE FORMS
We consider symmetric d-linear forms of dimension n over an algebraically closed field k of characteristic 0. The " center " of a form is the analogous of the space of symmetric matrices of a bilinear form. For d > 2 the center is a commutative subalgebra of Mn(k). The automorphism group of the form acts naturally on the center. We give a description of this group via this action.
متن کاملAutomorphism groups of polycyclic-by-finite groups and arithmetic groups
We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construc...
متن کاملThe Tensor Degree of a Pair of Finite Groups
In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.04.019