Alexander Moretó

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math.GR2026

The number of Sylow subgroups and a generalization of Mersenne primes

Jorge JimÃ©nez Urroz, Alexander MoretÃ³

Fix an integer $m$ bigger than 2. We prove that if there exists a finite group with $m p + 1$ Suylow $p$ -subgroups, where $p$ is large enough, then $m p + 1$ is prime. This improves on a…

math.GR2024

Fixed point ratios, Sylow numbers and coverings of $p$ -elements in finite groups

Robert M. Guralnick, Attila MarÃ³ti, Juan MartÃnez Madrid +2

Fixed point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a p…

math.GR2024

The codegree isomorphism problem for finite simple groups II

Nguyen N. Hung, Alexander MoretÃ³

Let $H$ be a nonabelian finite simple group. Huppert's conjecture asserts that if $G$ is a finite group with the same set of complex character degrees as $H$ , then $G\cong H\times…

math.GR2024

A normal version of Brauer's height zero conjecture

Alexander MoretÃ³, A. A. Schaeffer Fry

The celebrated ItÃ´-Michler theorem asserts that a prime $p$ does not divide the degree of any irreducible character of a finite group $G$ if and only if $G$ has a normal and abeli…

The number of Sylow subgroups and a generalization of Mersenne primes

Fixed point ratios, Sylow numbers and coverings of p-elements in finite groups

The codegree isomorphism problem for finite simple groups II

A normal version of Brauer's height zero conjecture

Fixed point ratios, Sylow numbers and coverings of $p$ -elements in finite groups