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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 prime $p$ and a finite group $G$, we use fixed point ratios to study th
Externí odkaz:
http://arxiv.org/abs/2407.20355
Autor:
Hung, Nguyen N., Moretó, Alexander
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 $G\cong H\times A$ for some abelian group $A$. Over the past two decades, several spec
Externí odkaz:
http://arxiv.org/abs/2406.10398
The celebrated It\^o-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 abelian Sylow $p$-subgroup. The principal block case of the recently-prove
Externí odkaz:
http://arxiv.org/abs/2406.06428
Autor:
Esmaili-Dokht, Pouya, Sgherzi, Francesco, Girelli, Valeria Soldera, Boixaderas, Isaac, Carmin, Mariana, Monemi, Alireza, Armejach, Adria, Mercadal, Estanislao, Llort, German, Radojkovic, Petar, Moreto, Miquel, Gimenez, Judit, Martorell, Xavier, Ayguade, Eduard, Labarta, Jesus, Confalonieri, Emanuele, Dubey, Rishabh, Adlard, Jason
The Memory stress (Mess) framework provides a unified view of the memory system benchmarking, simulation and application profiling. The Mess benchmark provides a holistic and detailed memory system characterization. It is based on hundreds of measure
Externí odkaz:
http://arxiv.org/abs/2405.10170
Autor:
Rebello, A. M., Ruela, L. M., Moreto, G., Klein, N. Y., Martins, E., Oliveira, I. S., Rouxinol, F., Sinnecker, J. P.
This paper explores methods to enhance the reproducibility of Josephson junctions, crucial elements in superconducting quantum technologies, when employing the Dolan technique in 30 kV e-beam processes. The study explores the influence of dose distri
Externí odkaz:
http://arxiv.org/abs/2403.19614
Recently, Malle and Navarro obtained a Galois strengthening of Brauer's height zero conjecture for principal $p$-blocks when $p=2$, considering a particular Galois automorphism of order~$2$. In this paper, for any prime $p$ we consider a certain elem
Externí odkaz:
http://arxiv.org/abs/2402.08361
Autor:
Moretó, Alexander
Let $G$ be a finite group. We study the generalized character defined by $\Xi(g)=|G|o(g)$, for $g\in G$, which is closely related to a function that has been very studied recently from a group theoretical point of view.
Externí odkaz:
http://arxiv.org/abs/2312.00008
Autor:
Moretó, Alexander
Let $G$ be a finite solvable group. We prove that if $\chi\in{\rm Irr}(G)$ has odd degree and $\chi(1)$ is the minimal degree of the non-linear irreducible characters of $G$, then $G/{\rm Ker} \chi$ is nilpotent-by-abelian.
Externí odkaz:
http://arxiv.org/abs/2310.05579
Problem 21 of Brauer's list of problems from 1963 asks whether for any positive integer k there are finitely many isomorphism classes of groups that occur as the defect group of a block with k irreducible characters. We solve this problem for princip
Externí odkaz:
http://arxiv.org/abs/2310.00134
We prove that there exists a universal constant $D$ such that if $p$ is a prime divisor of the index of the Fitting subgroup of a finite group $G$, then the number of conjugacy classes of G is at least $Dp/log_2 p$. We conjecture that we can take $D=
Externí odkaz:
http://arxiv.org/abs/2307.05579