On p-covalenced association schemes

  • Authors:

  • Mitsugu Hirasaka;Kyoung-tark Kim

  • Affiliations:

  • Department of Mathematics, Pusan National University, Jang-jeon dong, Busan, Republic of Korea;Department of Mathematics, Pusan National University, Jang-jeon dong, Busan, Republic of Korea

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2011

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Abstract

Let (X,S) denote an association scheme where X is a finite set. For a prime p we say that (X,S) is p-covalenced (p-valenced) if every multiplicity (valency, respectively) of (X,S) is a power of p. In the character theory of finite groups Ito's theorem states that a finite group G has a normal abelian p-complement if and only if every character degree of G is a power of p. In this article we generalize Ito's theorem to p-valenced association schemes, i.e., a p-valenced association scheme (X,S) has a normal p-covalenced p-complement if and only if (X,S) is p-covalenced.