Almost all wreath product character values are divisible by given primes

TL;DR

This paper proves that for large wreath product groups, nearly all character table entries are divisible by a prime p, extending previous results on symmetric groups.

Contribution

It generalizes the divisibility properties of character tables from symmetric groups to wreath products with symmetric groups.

Findings

Almost all character values in G wr S_N are divisible by p as N grows large.

Extends Peluse and Soundararajan's results from S_N to wreath products.

Provides asymptotic divisibility properties for character tables.

Abstract

For a finite group $G$ with integer-valued character table and a prime $p$, we show that almost every entry in the character table of $G \wr S_N$ is divisible by $p$ as $N \to \infty$. This result generalizes the work of Peluse and Soundararajan on the character table of $S_N$.