Macedo Lins de Araujo, Paula
Published in
Journal of Group Theory

This is the first of two papers in which we introduce and study two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. One of these zeta functions encodes the numbers of isomorphism classes of irreducible complex representations of finite dimensions of congruence quotients of the associated group...

Madanha, Sesuai Yash
Published in
Journal of Group Theory

We classify finite non-solvable groups with a faithful primitive irreducible complex character that vanishes on a unique conjugacy class. Our results answer a question of Dixon and Rahnamai Barghi and suggest an extension of Burnside’s classical theorem on zeros of characters.

Romero, Nadia
Published in
Journal of Group Theory

We explore conditions for the Frobenius–Wielandt morphism to commute with the operations of deflation and tensor induction on the Burnside ring. In doing this, we review the commutativity with induction. The techniques used for induction and tensor induction no longer work for deflation, so, in this case, we make use of tools coming from the theory...

Costoya, Cristina Méndez, David Viruel, Antonio
Published in
Journal of Group Theory

Let X be a finite type A n 2 {A_{n}^{2}} -polyhedron, n ≥ 2 {n\geq 2} . In this paper, we study the quotient group ℰ ( X ) / ℰ * ( X ) {\mathcal{E}(X)/\mathcal{E}_{*}(X)} , where ℰ ( X ) {\mathcal{E}(X)} is the group of self-homotopy equivalences of X and ℰ * ( X ) {\mathcal{E}_{*}(X)} the subgroup of self-homotopy equivalences inducing the...

Delizia, Costantino Shumyatsky, Pavel Tortora, Antonio
Published in
Journal of Group Theory

Let w be a group-word. For a group G, let G w {G_{w}} denote the set of all w-values in G and w ( G ) {w(G)} the verbal subgroup of G corresponding to w. The word w is semiconcise if the subgroup [ w ( G ) , G ] {[w(G),G]} is finite whenever G w {G_{w}} is finite. The group G is an FC ( w ) {\mathrm{FC}(w)} -group if the set of conjugates x G...

Delizia, Costantino Shumyatsky, Pavel Tortora, Antonio
Published in
Journal of Group Theory

Let w be a group-word. For a group G, let G w {G_{w}} denote the set of all w-values in G and w ( G ) {w(G)} the verbal subgroup of G corresponding to w. The word w is semiconcise if the subgroup [ w ( G ) , G ] {[w(G),G]} is finite whenever G w {G_{w}} is finite. The group G is an FC ( w ) {\mathrm{FC}(w)} -group if the set of conjugates x G...

Romero, Nadia
Published in
Journal of Group Theory

We explore conditions for the Frobenius–Wielandt morphism to commute with the operations of deflation and tensor induction on the Burnside ring. In doing this, we review the commutativity with induction. The techniques used for induction and tensor induction no longer work for deflation, so, in this case, we make use of tools coming from the theory...

Kolesnikov, Sergey Leontiev, Vladimir Egorychev, Georgy
Published in
Journal of Group Theory

Let G be a group, x , y ∈ G {x,y\in G} , and H is a normal closure in G of the subgroup generated by all commutators of x , y {x,y} that include more than two occurrences of y. Our main result is a parametrization of the uncollected part of Hall’s collection formula for ( x y ) n {(xy)^{n}} and two different collection formulas modulo H in an exp...

Bors, Alexander
Published in
Journal of Group Theory

We study finite groups G such that the maximum length of an orbit of the natural action of the automorphism group Aut ( G ) {\mathrm{Aut}(G)} on G is bounded from above by a constant. Our main results are the following: Firstly, a finite group G only admits Aut ( G ) {\mathrm{Aut}(G)} -orbits of length at most 3 if and only if G is cyclic of on...

Traustason, Gunnar Williams, James
Published in
Journal of Group Theory

In this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full cl...