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

Mikhail Muzychuk, Paul Hermann Zieschang

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9 Scopus citations

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 languageEnglish
Pages (from-to)3097-3103
Number of pages7
JournalDiscrete Mathematics
Volume308
Issue number14
DOIs
StatePublished - 28 Jul 2008
Externally publishedYes

Keywords

  • Association scheme
  • Schurian
  • Weakly closed involution

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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