A note on restriction of Characters of Alternating groups to Sylow Subgroups

TL;DR

This paper investigates how irreducible characters of alternating groups behave when restricted to Sylow p-subgroups, focusing on the number of linear constituents that appear in such restrictions.

Contribution

It provides new insights into the structure of irreducible characters of alternating groups upon restriction to Sylow p-subgroups, specifically analyzing the count of linear constituents.

Findings

Determined the number of linear constituents in restrictions of irreducible characters.

Identified conditions under which the number of linear constituents varies.

Enhanced understanding of character restrictions in the context of alternating groups.

Abstract

We restrict irreducible characters of alternating groups of degree divisible by $p$ to their Sylow $p$-subgroups and study the number of linear constituents.