Abstract

Speaker: Paul-Hermann Zieschang, University of Texas at Brownsville

Title: Sylow's Theorems for Association Schemes

Abstract: Let p be a prime number, and let G be an association scheme. An element g in G is called p-valenced if n_g is a power of p. A closed subset H of G is called p-valenced if each element of H is p-valenced. It is called a p-subset if it p-valenced and n_H is a power of p. It is called a Sylow p-subset if p does not divide n_G/n_H. Let us write Syl_p(G) in order to denote the set of all Sylow p-subsets of G. In my talk, I will prove that, if G is p-valenced, p divides |Syl_p(G)|-1, thereby generalizing Sylow's well-known theorems on finite groups.

Reference: A generalization of Sylow's theorems on finite groups to association schemes. Math. Z. 241, 665 672 (2002).