In the present note, we investigate schemes S in which each element s satisfies ns ≤ 2 and ns* s ≠ 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) 403-420] with the help of the largest normal subgroup of G having odd order.
- Association scheme
- Weakly closed involution
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics