Real characters in blocks
Laszlo Hethelyi, Erzsebet Horvath, Endre Szabo

TL;DR
This paper investigates real versions of key conjectures in block theory, proving specific cases for 2-blocks and characterizing classes related to defect groups.
Contribution
It introduces the real versions of Brauer's, Olsson's, and Eaton's conjectures and proves Eaton's conjecture for certain 2-blocks, also characterizing G-classes and related structures.
Findings
Proved the real Eaton's conjecture for 2-blocks with cyclic defect groups.
Characterized G-classes, real, and rational G-classes of defect groups.
Established conditions for principal 2-blocks with trivial real core.
Abstract
We consider real versions of Brauer's k(B) conjecture, Olsson's conjecture and Eaton's conjecture. We prove the real version of Eaton's conjecture for 2-blocks of groups with cyclic defect group and for the principal 2-blocks of groups with trivial real core. We also characterize G-classes, real and rational G-classes of the defect group of a block B.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems
