Non-induced modular representations of cyclic groups

Abstract

We compute the ring of non-induced representations for a cyclic group, Cn , over an arbitrary field and show that it has rank φ ( n ) , where φ is Euler’s totient function—independent of the characteristic of the field. Along the way, we obtain a “pick-a-number” trick; expressing an integer n as a sum of products of p-adic digits of related integers.