X
تبلیغات
( ریاضی بیست ) - نمونه سوالات کارشناسی ارشد ریاضی

جمعه بیستم اردیبهشت 1387

نمونه سوالات کارشناسی ارشد ریاضی



Finite Groups

Midterm MSc. Exam

Department of Mathematics Ferdowsi University of Mashhad

27 November 2007

A. Erfanian


1. a. Define k-transitive and k-homogenous group .

b. Prove that if G is transitive and for every is (k-1)-transitive, then G is k-transitive.

c. Give an example of a Double transitive groups.

2. a. Define a non-trivial block and give an example.

b. Prove that if and are two blocks of , then is also a block of G.

c. is it true the union of two blocks are always a block?

3. a. Define a primitive and imprimitive group and give an example for each.

b. Let be a transitive group. Then prove that if for every is a maximal subgroup of G, then is primitive.

4. a. Define a transvection and prove that if is a linear functional and is a linear transformation by the rule is a transvection on a suitable hyperplan H and .

b. Prove that can be generated by transvections.

c. Compute the order of groups

نوشته شده توسط ( نبی اله ابراهيمي) در 12:52 بعد از ظهر |  لینک ثابت   •