arXiv subjects

Nicola Grittini

Publications and source records attributed to Nicola Grittini.

3 recordsLinked to original sources

arXiv2022

On the degrees of irreducible characters fixed by some field automorphism, p-solvable groups

It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow $2$-subgroup. We generalize this result for Sylow $p$-subgroups, for any prime number $p$, while assuming the group to be $p$-solvable. In particular, it is proved that a $p$-solvable group has a normal Sylow $p$-subgroup if $p$ does not divide the degree of any irreducible character of the group fixed by a field automorphism of order $p$.

math.GR↗

arXiv2022

Sylow normalizers and irreducible characters with small cyclotomic field of values

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.

math.GR↗

arXiv2020

A note on cut groups of odd order

A group $G$ is said to be cut if, for every $g \in G$, each generator of $< \! g \! >$ is conjugated to either $g$ or $g^{-1}$. It is conjectured that a Sylow 3-subgroup $P$ of a cut group $G$ is cut. We prove that this is true if $|G|$ is odd.

math.GR↗