On association schemes all elements of which have valency 1 or 2

In the present note, we investigate schemes S in which each element s satisfies ns 2 and nss = 2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G// t , where G is a finite group and t an involution of G weakly closed in CG(t). Groups G with an involution t weakly closed in CG(t) have been described in Glauberman's Z-Theorem [G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Mikhail E. Muzychuk, Paul-Hermann Zieschang
• Keywords: DM 2008, Finite Group, Present Note, Weakly Closed