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Xiaoyou Chen

Publications and source records attributed to Xiaoyou Chen.

11 recordsLinked to original sources
arXiv2026

Some Remarks on Super $M_{p}$-groups

Let $G$ be a finite group and $p$ be a prime divisor of $|G|$. An irreducible $p$-Brauer character $φ$ of $G$ is called super-monomial if every primitive $p$-Brauer character inducing $φ$ is linear. The group $G$ is said to be a super $M_{p}$-group if every irreducible $p$-Brauer character of $G$ is super-monomial. In this note, we investigate the conditions under which a finite group $G$ qualifies as a super $M_{p}$-group. We demonstrate that every normal subgroup of a super $M_{p}$-group of odd order is an $M_{p}$-group.

math.GR↗
arXiv2026

QuantEval: A Benchmark for Financial Quantitative Tasks in Large Language Models

Large Language Models (LLMs) have shown strong capabilities across many domains, yet their evaluation in financial quantitative tasks remains fragmented and mostly limited to knowledge-centric question answering. We introduce QuantEval, a benchmark that evaluates LLMs across three essential dimensions of quantitative finance: knowledge-based QA, quantitative mathematical reasoning, and quantitative strategy coding. Unlike prior financial benchmarks, QuantEval integrates a CTA-style backtesting framework that executes model-generated strategies and evaluates them using financial performance metrics, enabling a more realistic assessment of quantitative coding ability. We evaluate some state-of-the-art open-source and proprietary LLMs and observe substantial gaps to human experts, particularly in reasoning and strategy coding. Finally, we conduct large-scale supervised fine-tuning and reinforcement learning experiments on domain-aligned data, demonstrating consistent improvements. We hope QuantEval will facilitate research on LLMs' quantitative finance capabilities and accelerate their practical adoption in real-world trading workflows. We additionally release the full deterministic backtesting configuration (asset universe, cost model, and metric definitions) to ensure strict reproducibility.

cs.CL↗
arXiv2025

A converse for a theorem of Gallagher

Let $G$ be a finite group. Suppose $N$ is a normal subgroup of $G$. Recall that Gallagher's theorem states that if $χ\in {\rm Irr} (G)$ satisfies $χ_N$ is irreducible, then $χβ$ is irreducible and distinct for all $β\in {\rm Irr} (G/N)$. Furthermore, if $θ= χ_N$, then these are all of the irreducible constituents of $θ^G$. We prove that the converse of this theorem holds. We also prove that a partial converse of the Brauer version of this theorem holds. Finally, we prove that an analog of Gallagher's theorem holds for Isaacs' $π$-partial characters and that a partial converse of that theorem is true.

math.GR↗
arXiv2025

Isaacs' Generalization of Taketa's theorem

We generalize the definition of pseudo monomial characters and $M$-groups to the Brauer character and Isaacs' $π$-partial character settings. We prove an analogs of Isaacs's generalization of Taketa's theorem in those settings. We consider other analogs of results regarding $M$-groups in those settings.

math.GR↗
arXiv2025

$M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees

Let $G$ be a finite group and $p$ be a prime. We prove that if $G$ has three codegrees, then $G$ is an $M$-group. We prove for some prime $p$ that if every irreducible Brauer character of $G$ is a prime, then for every normal subgroup $N$ of $G$ either $G/N$ or $N$ is an $M_p$-group.

math.GR↗
arXiv2018

Some properties of various graphs associated with finite groups

In this paper we have investigated some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it has been shown that the simple group $L_2(7)$ can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we have obtained an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.

math.GR↗
arXiv2017

Itô's theorem and monomial Brauer characters

Let $G$ be a finite solvable group, and let $p$ be a prime. In this note, we prove that $p$ does not divide $φ(1)$ for every irreducible monomial $p$-Brauer character $φ$ of $G$ if and only if $G$ has a normal Sylow $p$-subgroup.

math.GR↗
arXiv2017

Groups with one or two super-Brauer character theories

A super-Brauer character theory of a group $G$ and a prime $p$ is a pair consisting of a partition of the irreducible $p$-Brauer characters and a partition of the $p$-regular elements of $G$ that satisfy certain properties. We classify the groups and primes that have exactly one super-Brauer character theory. We discuss the groups with exactly two super-Brauer character theories.

math.GR↗
arXiv2017

Upper and lower bounds on Chillag table sums

Chillag has showed that there is a single generalization showing that the sums of ordinary character tables, Brauer character, and projective indecomposable characters are positive integers. We show that Chillag's construction also applies to Isaacs' $π$-partial characters. We show that if an extra condition is assumed, then we can obtain upper and lower bounds on the Chillag's table sums. We will demonstrate that this condition holds for Brauer characters, $π$-partial characters, and projective indecomposable characters, and so we obtain upper and lower bounds for the table sums in those cases. We also obtain results regarding the sums of rows and columns in these tables.

math.GR↗