This paper introduces the concept of Artin semigroup a large (extra large) type. We prove their injective embedding in corresponding groups type and solvability word conjugacy problem this class semigroups.

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture. Introduction Let ρ : Gal(Q/Q) → GLn(C) be an irreducible continuous representation of the absolute Galois group of Q. Brauer [2]...

The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

In this paper, we study the discrete logarithm problem in the finite fields Fqn where n|q−1. The field is called a Kummer field or a Kummer extension of Fq. It plays an important role in improving the AKS primality proving algorithm. It is known that we can efficiently construct an element g with order greater than 2 in the fields. Let Sq(•) be the function from integers to the sum of digits in...

There are well-known monomorphisms between the Artin groups of finite type An, Bn = Cn and affine type Ãn−1, C̃n−1. The Artin group A(An) is isomorphic to the (n + 1)strand braid group Bn+1, and the other three Artin groups are isomorphic to some subgroups of Bn+1. The inclusions between these subgroups yield monomorphisms A(Bn) → A(An), A(Ãn−1) → A(Bn) and A(C̃n−1) → A(Bn). There are another typ...

For each d ∈ N we construct a 3-generated group Hd, which is a subdirect product of free groups, such that the cohomological dimension of Hd is d. Given a group F and a normal subgroup N C F we prove that any right angled Artin group containing the special HNN-extension of F with respect to N must also contain F/N . We apply this to construct, for every d ∈ N, a 4-generated group Gd, embeddable...

The result of this paper is the determination of the cohomology of Artin groups of type An, Bn and Ãn with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type Bn with coefficients over the module Q[q±1, t±1]. Here the first n− 1 standard generators of the group act by (−q)-multiplication, while the last one acts by (−t)-multipl...