arXiv subjects

Lee Tae Young

Publications and source records attributed to Lee Tae Young.

4 recordsLinked to original sources

arXiv2026

Finite groups with many elements of the same order

We study a conjecture by Deaconescu on the solubility of finite groups with claims that if more than half of the elements in a finite group has the same order $k$, then the group is soluble. We show that the original conjecture fails by presenting some counterexamples. By restricting to a fixed $k$, the conjecture may or may not hold depending on $k$. We prove that if $k$ is a power of a prime other than $2$ or $3$, or if $k=2, 3$ or $4$, then the conjecture holds, while it fails for many other choices of $k$ including all multiples of $2$ and $3$ which are larger than $5$. For $k=4$ we also find the sharp upper bound of the ratio of elements of order $4$ in non-soluble groups. We also prove that for all $k>1$, it is always possible to find a finite non-soluble group where at least $2/15$ of the elements have order $k$.

math.GR↗

arXiv2026

Relations between values and zeros of irreducible characters of symmetric groups

We prove certain polynomial relations between the values of complex irreducible characters of general finite symmetric groups. We use it to find some sets of conjugacy classes such that no finite symmetric group has a complex irreducible character that vanishes at every class in the set. In particular, we show that if $n$ satisfies certain conditions, then $S_n\setminus \{1\}$ cannot be covered by the set of zeros of three irreducible characters. We also prove that the values of character of $2$-defect zero can be expressed as rational functions in $n$, and build a recursive algorithm to find these rational functions. As another application, we improve a result by A. Miller on identification of irreducible characters by checking small number of values.

math.RT↗

arXiv2024

Hypergeometric sheaves and extraspecial groups in even characteristic

We determine precisely which irreducible hypergeometric sheaves have an extraspecial normalizer in characteristic 2 as their geometric monodromy groups. This resolves the last open case of the determination of local monodromy at 0 of irreducible hypergeometric sheaves with finite geometric monodromy group.

math.GR↗

arXiv2023

Hypergeometric Sheaves and General Linear Groups

We find all irreducible hypergeometric sheaves whose geometric monodromy group is finite, almost quasisimple and has the projective special linear group $PSL_n(q)$ with $n\geq 3$ as a composition factor. We use the classification of semisimple elements with specific spectra in irreducible Weil representations to prove that if an irreducible hypergeometric sheaf has such geometric monodromy group, then it must be of certain form. Then we extend results of Katz and Tiep on a prototypical family of such sheaves to full generality to show that these hypergeometric sheaves do have such geometric monodromy groups, and that they have some connection to a construction of Abhyankar.

math.GR↗