Minimal logarithmic signatures for classical groups
The minimal logarithmic signature conjecture states that in any finite simple group there are subsets A (i) , 1 a parts per thousand currency sign i a parts per thousand currency sign k such that the size |A (i) | of each A (i) is a prime or 4 and each element of the group has a unique expression as a product of elements. The conjecture is known to be true for several families of simple groups. In this paper the conjecture is shown to be true for the groups, when q is even, by studying the action on suitable spreads in the corresponding projective spaces. It is also shown that the method can be used for the finite symplectic groups. The construction in fact gives cyclic minimal logarithmic signatures in which each A (i) is of the form for some element y (i) of order a parts per thousand yen |A (i) |.
logarithmic signatures finite simple groups spreads finite classical groups