The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups

Abstract

A logarithmic signature for a finite group G is a sequence [A1,? ,As] of subsets of G such that every element g?G can be uniquely written in the form g=g1?gs, where gi?Ai, 1≤i≤s. The aim of this paper is proving the existence of an MLS for the Suzuki simple groups Sz(22m+1), m>1, when 22m+1+2m+1+1 or 22m+1?2m+1+1 are primes. The existence of an MLS for untwisted group G2(4) and the sporadic Suzuki group Suz are also proved. As a consequence of our results, we prove that the simple groups have an MLS.