Abstract
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.
Original language | English |
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Pages (from-to) | 3097-3103 |
Number of pages | 7 |
Journal | Discrete Mathematics |
Volume | 308 |
Issue number | 14 |
DOIs | |
State | Published - 28 Jul 2008 |
Externally published | Yes |
Keywords
- Association scheme
- Schurian
- Weakly closed involution
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics