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

In the present note, we investigate schemes S in which each element s satisfies image and image. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to image, where G is a finite group and t an involution of G weakly closed in image. Groups G with an involution t weakly closed in image have been described in Glaubermanʹs image-Theorem [G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403–420] with the help of the largest normal subgroup of G having odd order.