On the number of characters in blocks of quasi-simple groups

TL;DR

This paper establishes inequalities relating key invariants of Brauer p-blocks in finite quasi-simple groups for primes p ≥ 5, providing explicit calculations and bounds for classical groups.

Contribution

It introduces new inequalities and explicit bounds for invariants of Brauer p-blocks in quasi-simple groups, advancing understanding of their structure.

Findings

Proved inequalities between block invariants for primes p ≥ 5

Explicitly determined or bounded invariants for classical groups

Enhanced understanding of the structure of Brauer p-blocks

Abstract

We prove, for primes $p\ge5$, two inequalities between the fundamental invariants of Brauer $p$-blocks of finite quasi-simple groups: the number of characters in the block, the number of modular characters, the number of height zero characters, and the number of conjugacy classes of a defect group and of its derived subgroup. For this, we determine these invariants explicitly, or at least give bounds for them for several classes of classical groups.