The maximum distinguishing number of a group

Details The maximum distinguishing number of a group The maximum distinguishing number of a group

2006-01-14

arxiv.org/abs/math/0601359v1

Mathematics

Combinatorics

9 pages, to appear in Electronic J. Combinatorics

Scientific paper

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.

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