Publications of Hegedűs, Pál

Determination of conjugacy class sizes from products of characters

In [5] Robinson showed that the character degrees are determined by knowing, for all n, the number of ways that the identity can be expressed as a product of n commutators. Earlier, in [6], Strunkov showed that the existence of characters of p-defect 0 can be determined by counting solutions to certain equations involving commutators and conjugates. In this paper, we prove analogs to Robinson’s and Strunkov’s theorems by switching conjugacy classes and characters. We show that counting the multiplicity of the trivial character in certain products of characters determines the conjugacy class sizes and existence of conjugacy classes with p-defect 0.

The constants of the Volterra derivation

The ring of constants of the Volterra derivation is determined. Confirming a conjecture of Zieli\'nski, it is always a polynomial ring.