On The Critical Number Of Finite Groups (II)

Abstract

Let \(G\) be a finite group and \(S \subseteq G \setminus \{0\}\). 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 \(G \setminus \{0\}\) 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 \(2\).