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math.RA2025
On a question by Roggenkamp about group algebras
Dylan Johnston, Dmitriy Rumynin
We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in…
math.GR2025
Brauer's 14th Problem and Dyson's Tenfold Way
Dmitriy Rumynin, James Taylor
We consider Brauer's 14th Problem in the context of "Real" structures on finite groups and their antilinear representations. The problem is to count the number of characters of eac…