-groups, diagonalizable automorphisms and loops
Parallelepipeds, nilpotent groups and Gowers norms
In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions and and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.
Partial Homogeneity in Locally Finite Groups.
p-Brauer characters of q-Defect 0.
Perfect numbers and finite groups
Periodic factorization of a finite Abelian 2-group.
Periodic groups saturated by the group .
Periodic groups saturated with the groups .
Periodic linear groups factorized by mutually permutable subgroups
The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic...
Permutability of centre-by-finite groups
Let be a group and be an integer greater than or equal to . is said to be -permutable if every product of elements can be reordered at least in one way. We prove that, if has a centre of finite index , then is -permutable. More bounds are given on the least such that is -permutable.
Permutable Subgroups of Infinite Groups.
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
Polarities of G. Higman's symmetric design and a strongly regular graph on 176 vertices.
Polynomial and Term Functions over Groups with Coprime Chief Factors.
Polynomials over the permutation group of three elements
Présentation de certains couples fischériens de type classique
Presentations of finite simple groups: a computational approach
All finite simple groups of Lie type of rank over a field of size , with the possible exception of the Ree groups , have presentations with at most 49 relations and bit-length . Moreover, and have presentations with 3 generators; 7 relations and bit-length , while has a presentation with 6 generators, 25 relations and bit-length .
Prime Characters and Factorizations of Quasi-Primitive Characters.
Prime divisors of conjugacy class lengths in finite groups
We show that in a finite group which is -nilpotent for at most one prime dividing its order, there exists an element whose conjugacy class length is divisible by more than half of the primes dividing .
Prime graph components of finite almost simple groups