arXiv subjects

M. J. Felipe

Publications and source records attributed to M. J. Felipe.

6 recordsLinked to original sources

arXiv2024

Groups whose common divisor graph on $p$-regular classes has diameter three

Let $G$ be a finite $p$-separable group, for some fixed prime $p$. Let $\Gamma_p(G)$ be the common divisor graph built on the set of non-central conjugacy classes of $p$-regular elements of $G$: this is the graph whose vertices are the conjugacy classes of those non-central elements of $G$ such that $p$ does not divide their orders, and two distinct vertices are adjacent if and only if the greatest common divisor of their lengths is strictly greater than one. The aim of this paper is twofold: to positively answer an open question concerning the maximum possible distance in $\Gamma_p(G)$ between a vertex with maximal cardinality and any other vertex, and to study the $p$-structure of $G$ when $\Gamma_p(G)$ has diameter three.

math.GR↗

arXiv2019

On zeros of irreducible characters lying in a normal subgroup

Let $N$ be a normal subgroup of a finite group $G$. In this paper, we consider the elements $g$ of $N$ such that $χ(g)\neq 0$ 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 also study certain arithmetical properties of the $G$-conjugacy class sizes of the elements of $N$ which are zeros of some irreducible character of $G$. In particular, if $N=G$, then new contributions are obtained.

math.GR↗

arXiv2018

Products of groups and class sizes of $π$-elements

We provide structural criteria for some finite factorised groups $G = AB$ when the conjugacy class sizes in $G$ of certain $π$-elements in $A\cup B$ are either $π$-numbers or $π'$-numbers, for a set of primes $π$. In particular, we extend for products of groups some earlier results.

math.GR↗

arXiv2018

Zeros of irreducible characters in factorised groups

An element $g$ of a finite group $G$ is said to be vanishing in $G$ if there exists an irreducible character $χ$ of $G$ such that $χ(g)=0$; in this case, $g$ is also called a zero of $G$. The aim of this paper is to obtain structural properties of a factorised group $G=AB$ when we impose some conditions on prime power order elements $g\in A\cup B$ which are (non-)vanishing in $G$.

math.GR↗

arXiv2017

Prime power indices in factorised groups

Let the group $G = AB$ be the product of the subgroups $A$ and $B$. We determine some structural properties of $G$ when the $p$-elements in $A\cup B$ have prime power indices in $G$, for some prime $p$. More generally, we also consider the case that all prime power order elements in $A\cup B$ have prime power indices in $G$. In particular, when $G = A = B$ we obtain as a consequence some known results.

math.GR↗

arXiv2017

Square-free class sizes in products of groups

We obtain some structural properties of a factorised group $G = AB$, given that the conjugacy class sizes of certain elements in $A\cup B$ are not divisible by $p^2$, for some prime $p$. The case when $G = AB$ is a mutually permutable product is especially considered.

math.GR↗