Search results for "Finite group"
showing 10 items of 205 documents
Characters of 𝑝’-degree with cyclotomic field of values
2006
If p p is a prime number and G G is a finite group, we show that G G has an irreducible complex character of degree not divisible by p p with values in the cyclotomic field Q p \mathbb {Q}_p .
Rationality and Sylow 2-subgroups
2010
AbstractLet G be a finite group. If G has a cyclic Sylow 2-subgroup, then G has the same number of irreducible rational-valued characters as of rational conjugacy classes. These numbers need not be the same even if G has Klein Sylow 2-subgroups and a normal 2-complement.
A self-centralizing characteristic subgroup
1989
AbstractIn this note we introduce a self-centralizing characteristic subgroup, associated with quasinilpotent injectors, of a finite group.
On zeros of characters of finite groups
2018
We survey some results concerning the distribution of zeros in the character table of a finite group and its influence on the structure of the group itself.
A note on maximal subgroups and conjugacy classes of finite groups
2021
Given a finite group G, two elements are ≡m-related if they lie in exactly the same maximal subgroups of G. This equivalence relation was introduced by P. J. Cameron, A. Lucchini and C. M. Roney-Do...
On finite minimal non-nilpotent groups
2005
[EN] A critical group for a class of groups X is a minimal non-X-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of GolÂżfandÂżs theorem on maximal Schmidt groups.
A generalization to Sylow permutability of pronormal subgroups of finite groups
2020
[EN] In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, or groups in which Sylow permutability is a transitive relation, can be characterized in terms of this property, in a similar way as T-groups, or groups in which normality is transitive, can be characterized in terms of pronormality.
On minimal subgroups of finite groups
1996
Decomposition numbers and local properties
2020
Abstract If G is a finite group and p is a prime, we give evidence that the p-decomposition matrix encodes properties of p-Sylow normalizers.
On defects of characters and decomposition numbers
2017
We propose upper bounds for the number of modular constituents of the restriction modulo [math] of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.