 # Nicola GrittiniUniversity of Florence | UNIFI · Dipartimento di Matematica e Informatica "Ulisse Dini"

Master of Science

9
Publications
705
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6
Citations
Introduction
Skills and Expertise
October 2017 - present Position
• Tutor
Description
• As a tutor, I both hold a teaching session, when I explain to the student how to solve exercises in Mathematics and I check that they are able to do them alone, and have receivement hours, during which I help students singularly
Education
October 2013 - February 2016

## Publications

Publications (9)
Preprint
Full-text available
We prove that, in a finite group, if every rational irreducible character has odd degree, then all rational elements are 2-elements, as it was originally conjectured by Tiep and Tong-Viet.
Article
In this paper, we prove the existence of a relation between the prime divisors of the order of a Sylow normalizer and the degree of characters having values in some small cyclotomic fields. This relation is stronger when the group is solvable.
Preprint
Full-text available
In this paper, we prove the existence of a relation between the prime divisors of the order of a Sylow normalizer and the degree of characters having values in some small cyclotomic fields. This relation is stronger when the group is solvable.
Preprint
Full-text available
It is known that, if all the irreducible real valued characters of a finite group are of odd degree, then the group has a normal Sylow 2-subgroup. In this paper, we prove and analogous result for solvable groups, by taking into account the degree of irreducible characters fixed by some field isomorphism of prime order $p$. We prove it as a conseque...
Article
If a group G is π-separable, where π is a set of primes, the set of irreducible characters B π ⁡ ( G ) ∪ B π ′ ⁡ ( G ) {\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)} can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito–Michler and Thompson’s theorem on characte...
Preprint
Full-text available
If a group $G$ is $\pi$-separable, where $\pi$ is a set of primes, the set of irreducible characters $\operatorname{B}_{\pi}(G) \cup \operatorname{B}_{\pi'}(G)$ can be defined. In this paper, we prove that there are variants of some classical theorems in character theory, namely the Theorem of Ito-Michler and Thompson theorem on character degrees,...
Article
Let G be a p-solvable group, where p is a prime. We prove that the p-length of G is less or equal then the number of distinct irreducible character degrees of G not divisible by p. Furthermore, we prove that the result still holds if we impose some restriction on the field of values of the characters. In particular, if p=2, we can consider only rat...
Preprint
Full-text available
Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that χ(g) ≠ 0 for all irreducible characters χ of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N has a normal Sylow p-subgroup. As a consequence, we al...
Article
Full-text available
Let N be a normal subgroup of a finite group G. An element g ∈ G such that χ(g) = 0 for some irreducible character χ of G is called a vanishing element of G. The aim of this paper is to analyse the influence of the π-elements in N which are (non-)vanishing in G on the π-structure of N , for a set of primes π. We also study certain arithmetical prop...