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

摘要

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