The Burnside problem for semigroups

Yet Another Solution to the Burnside Problem for Matrix Semigroups

We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.

Free Burnside Semigroups

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

On the Burnside Semigroups xn = xn+m

In this paper we prove that the congruence classes of A associated to the Burnside semigroup with jAj generators deened by the equation x n = x n+m , for n 4 and m 1, are recognizable. This problem was originally formulated by Brzozowski in 1969 for m = 1 and n 2. De Luca and Varricchio solved the problem for n 5 in 90. A little later, McCammond extended the problem for m 1 and solved it indepe...

The Restricted Burnside Problem

In 1902 William Burnside [5] wrote 'A still undecided point in the theory of discontinuous groups is whether the order of a group may be not finite, while the order of every operation it contains is finite'. In modern terminology the most general form of the problem is 'can a finitely generated group be infinite while every element in the group has finite order?'. This question was answered in ...