# Non-induced modular representations of cyclic groups

### Liam Jolliffe and Robert A. Spencer

**Abstract:**We compute the ring of non-induced representations for a cyclic group, \(C_n\), over an arbitrary field and show that it has rank \(\varphi(n)\), where \(\varphi\) 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.

A draft of this work is available on the ArXiv.

#### Cite with BibTex

```
@misc{jolliffe2021noninduced,
title={Non-induced modular representations of cyclic groups},
author={Liam Jolliffe and Robert A. Spencer},
year={2021},
eprint={2111.09187},
archivePrefix={arXiv},
primaryClass={math.RT}
}
```