THE TWISTED TWIN OF THE GRIGORCHUK GROUP

We study a twisted version of Grigorchuk's first group, and stress its similarities and differences to its model. In particular, we show that it admits a finite endomorphic presentation, has infinite-rank multiplier, and does not have the congruence property.

Arithmetic Functions Satisfying a Congruence Property

This note proves (in the theorem below) a conjecture made by the author last year through the pages of the Departmental Problem Book. This arose in connection with some other investigations of arithmetic functions.