Orders of elements and zeros and heights of characters in a finite group

dc.creatorWilde, Tom
dc.date2006-04-14
dc.date.accessioned2026-07-07T07:10:56Z
dc.date.available2026-07-07T07:10:56Z
dc.descriptionLet 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.description12 pages. Comments welcome
dc.identifierhttps://arxiv.org/abs/math/0604337
dc.identifierhttp://arxiv.org/abs/math/0604337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111577
dc.subjectRepresentation Theory
dc.subject20C15 (Primary), 20C20 (Secondary)
dc.titleOrders of elements and zeros and heights of characters in a finite group
dc.typetext

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