Existence of Minimal Logarithmic Signature for Finite Simple Groups

چکیده مقاله

A logarithmic signature (LS for short) of a finite group G is a sequence alpha = [A1;... ;As] of subsets of G such that every element g in G can be uniquely written in the form g = g1 ... gs, where gi in Ai, 1 leq i leq s. The number P is called the length of alpha and denoted by l(alpha). An observation by Gonzalez Vasco and Steinwandt shows that l(alpha) geq Pi. A logarithmic signature alpha is said to be minimal (MLS) if l(alpha) = P. In this talk, recent progress on this conjecture is reported. We also present an efficient algorithm for providing MLS for sporadic groups.