Controllability of Formation Systems on Special Orthogonal Groups Over Directed Graphs

commuting 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...

Orthogonal Structures in Directed Graphs

Invariant Theory of Special Orthogonal Groups

In this paper we study the action of SO.n/ on m-tuples of n n matrices by simultaneous conjugation. We show that the polynomial invariants are generated by traces and polarized Pfaffians of skewsymmmetric projections. We also discuss the same problem for other classical groups. 1 Special Orthogonal Groups Let F be a field of characteristic 0. If A is a skewsymmetric 2k 2k matrix over F , we den...

Orthogonal Groups over Local Rings

In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...

Survey on Controllability of Invariant Systems on Solvable Lie Groups

Known and new results on controllability of right-invariant systems on solvable Lie groups are presented and discussed. The main ideas and technique used are outlined, illustrating examples are given. Some open questions are suggested.