Degree graphs of simple orthogonal and symplectic groups
نویسندگان
چکیده
منابع مشابه
Degree Graphs of Simple Orthogonal and Symplectic Groups
Let G be a finite group and let cd(G) be the set of irreducible ordinary character degrees of G. The degree graph of G is the graph ∆(G) whose set of vertices is the set of primes dividing degrees in cd(G), with an edge between primes p and q if pq divides some degree in cd(G). We determine the graph ∆(G) for the finite simple groups of types B`, C`, D` and D`; that is, for the simple orthogona...
متن کاملcommuting and non -commuting graphs of finit groups
فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
15 صفحه اولInvariant Fields of Symplectic and Orthogonal Groups
The projective orthogonal and symplectic groups POn(F ) and PSpn(F ) have a natural action on the F vector space V ′ = Mn(F ) ⊕ . . . ⊕ Mn(F ). Here we assume F is an infinite field of characteristic not 2. If we assume there is more than one summand in V , then the invariant fields F (V )n and F (V )n are natural objects. They are, for example, the centers of generic algebras with the appropri...
متن کاملDegree Graphs of Simple Linear and Unitary Groups
Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph ∆(G) is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a ∈ cd(G). We determine the graph ∆(G) for the finite simple groups of types A`(q) and A`(q ), that is, for the simple linear and unitary gr...
متن کاملEigendistributions for Orthogonal Groups and Representations of Symplectic Groups
We consider the action of H = O(p, q) on the matrix space Mp+q,n(R). We study a certain orbit O of H in the null cone N ⊆ Mp+q,n(R) which supports an eigendistribution dνO for H . Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n,R)∼-cyclic module generated by dνO under the oscillator representation of G̃ (the metaplectic cover of G = Sp(2n(...
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: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.08.038