On The Critical Number of Finite Groups (II)

2012/12/04 by Qinghong Wang, Wang, Qinghong, Yongke Qu +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1212.0595

arxiv created 2012/12/04 · arxiv updated 2012/12/05

Abstract

Let G be a finite group and S a subset of G\0. We call S an additive basis of G if every element of G can be expressed as a sum over a nonempty subset in some order. Let cr(G) be the smallest integer t such that every subset of G\0 of cardinality t is an additive basis of G. In this paper, we determine cr(G) for the following cases: (i) G is a finite nilpotent group; (ii) G is a group of even order which possesses a subgroup of index 2.

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