Primitive permutation groups and a characterization of the odd 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...

On odd primitive graphs

In this paper, we prove that every odd primitive graph must contain two vertex disjoint odd cycles. We also characterize a family of odd primitive graphs whose exponent achieves the upper bound. We follow the notation and terminology of Bondy and Murty [1], unless otherwise stated. A digraph D is said to be primitive if there exists a positive integer k such that for each ordered pair of vertic...

Distinguishing Primitive Permutation Groups

Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.

Factorizations of Primitive Permutation Groups

On the Orders of Primitive Permutation Groups

The problem of bounding the order of a permutation group G in terms of its degree n was one of the central problems of 19th century group theory (see [4]). It is closely related to the 1860 Grand Prix problem of the Paris Academy, but its history goes in fact much further back (see e.g. [3], [1] and [10]). The heart of the problem is of course the case where G is a primitive group. The best res...