The maximum distinguishing number of a group
| dc.creator | Chan, Melody | |
| dc.date | 2006-01-14 | |
| dc.date.accessioned | 2026-07-07T06:58:55Z | |
| dc.date.available | 2026-07-07T06:58:55Z | |
| dc.description | Let 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.description | 9 pages, to appear in Electronic J. Combinatorics | |
| dc.identifier | https://arxiv.org/abs/math/0601359 | |
| dc.identifier | http://arxiv.org/abs/math/0601359 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107555 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 05E15 (Primary) 20B25, 20D60 (Secondary) | |
| dc.title | The maximum distinguishing number of a group | |
| dc.type | text |