Orders of elements and zeros and heights of characters in a finite group
| dc.creator | Wilde, Tom | |
| dc.date | 2006-04-14 | |
| dc.date.accessioned | 2026-07-07T07:10:56Z | |
| dc.date.available | 2026-07-07T07:10:56Z | |
| dc.description | Let χbe an irreducible character of the finite group G. If g is an element of G and χ(g) is not zero, then we conjecture that the order of g divides |G|/χ(1). The conjecture is a generalization of the classical fact that irreducible p-projective characters vanish on p-singular elements, since the latter is equivalent to saying that if χ(g) is not zero then the square free part of the order of g divides |G|/χ(1). We prove some partial results on the conjecture; in particular, we show that the order of g divides (|G|/χ(1))^2. Using these results, we derive some bounds on heights of characters. We also pose a related conjecture concerning congruences satisfied by central character values. | |
| dc.description | 12 pages. Comments welcome | |
| dc.identifier | https://arxiv.org/abs/math/0604337 | |
| dc.identifier | http://arxiv.org/abs/math/0604337 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111577 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C15 (Primary), 20C20 (Secondary) | |
| dc.title | Orders of elements and zeros and heights of characters in a finite group | |
| dc.type | text |