A note on critical sets for the elementary abelian 2-group

Abstract

In this note, we consider the problem of determining the sizes of critical sets in elementary abelian 2-groups. In particular, for the case of order 8, Cooper et al. have shown that the size of a minimal critical set cannot be less than 24. We provide some evidence for the conjecture that it is actually 26 and we show how critical sets of size 26 can be obtained constructively.