The Artin exponent induced from cyclic subgroups of finite groups was studied extensively by T.Y. Lam in [5]. A Burnside ring theoretic version of the results in [5] for p-groups was given in [6]. Here we shall be interested in looking at the Artin exponent induced from the elementary abelian subgroups of finite p-groups using some results of A. Dress in [3].

According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements σi are presented by the commutators of generators which are powers of commuting elements. Hence they are naturally presented as right-angled Artin groups. The case of subgroups generated by powers of the band generators aij is more involved. We show...

The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension grou...

Using the Burnside ring theoretic methods a new setting and a complete description of the Artin exponent A(G) of finite p-groups was obtained in [4]. In this paper, we compute A(G) for any finite group G – hence providing the global version of [4].

This paper finds the Artin characters and exponent dependingon character table conjugacy classes of projective special lineargroup PSL (2,P*).Then we prove that (2, P*) isequal to p*' where P is a prime number , p=3 k> 0.

in this article, we study the artin-rees property in  c(x), in the  rings of fractions of  c(x) and in the factor rings of c(x) . we show that c(x)/(f) is an artin-rees ring if and only if  z(f)  is an open p-space. a necessary and sufficient condition for the local rings of  c(x)   to be artin-rees rings is that each prime ideal in  c(x)  becomes minimal and it turns out that every local ring ...

This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the center, the word problem, and the cohomology (K(π, 1) problem). It is also an opportunity to prove three new results concerning these questions: (1) if all free of infinity Artin-Tits groups are torsion free, then all Artin-Tits groups will be torsion free; (2) If all free of infinity irreducible non-sph...

Artin groups (also known as Artin-Tits groups) are generalizations of Artin’s braid groups. This paper concerns Artin groups of spherical type, that is, those whose corresponding Coxeter group is finite, as is the case for the braid groups. We compute presentations for the commutator subgroups of the irreducible spherical-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the b...