The maximum distinguishing number of a group

dc.creatorChan, Melody
dc.date2006-01-14
dc.date.accessioned2026-07-07T06:58:55Z
dc.date.available2026-07-07T06:58:55Z
dc.descriptionLet G be a group acting faithfully on a set X. The distinguishing number of the action of G on X is the smallest number of colors such that there exists a coloring of X where no nontrivial group element induces a color-preserving permutation of X. In this paper, we show that if G is nilpotent of class c or supersolvable of length c then G always acts with distinguishing number at most c+1. We obtain that all metacyclic groups act with distinguishing number at most 3; these include all groups of squarefree order. We also prove that the distinguishing number of the action of the general linear group over a field K on the vector space K^n is 2 if K has at least n+1 elements.
dc.description9 pages, to appear in Electronic J. Combinatorics
dc.identifierhttps://arxiv.org/abs/math/0601359
dc.identifierhttp://arxiv.org/abs/math/0601359
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107555
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject05E15 (Primary) 20B25, 20D60 (Secondary)
dc.titleThe maximum distinguishing number of a group
dc.typetext

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