The paper introduces a conjectural framework for Alperin's Main Problem using Irr^x(G) character sets non-vanishing at given elements and Sub_G(x) subnormalizers, recovering McKay's conjecture and verifying the main statements for simple groups with TI Sylow p-subgroups.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.RT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Conjectures propose that the sets Irr^x(G) and subgroups Sub_G(x) are the natural objects attached to p-elements x for studying local character values in block theory.
citing papers explorer
-
Alperin's Main Problem of Block Theory
The paper introduces a conjectural framework for Alperin's Main Problem using Irr^x(G) character sets non-vanishing at given elements and Sub_G(x) subnormalizers, recovering McKay's conjecture and verifying the main statements for simple groups with TI Sylow p-subgroups.
-
The Main Problem of Block Theory: Picky Elements and Subnormalizers
Conjectures propose that the sets Irr^x(G) and subgroups Sub_G(x) are the natural objects attached to p-elements x for studying local character values in block theory.