Rational G-matrices with rational eigenvalues

Bridges, William; Mena, R. A.

doi:10.1016/0097-3165(82)90026-7

Cited by 62 publications

(45 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, by [2], the Schur ring is not primitive, contrary to Lemma 2.1. For (ii), see Corollary 2.5 of [3]. (iii) follows from (i) and (ii).…”

Section: Preliminariesmentioning

confidence: 77%

See 1 more Smart Citation

On Three-Dimensional Schur Rings Obtained from Partial Spreads

Hiramine

1997

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

“…Then, by [2], the Schur ring is not primitive, contrary to Lemma 2.1. For (ii), see Corollary 2.5 of [3]. (iii) follows from (i) and (ii).…”

Section: Preliminariesmentioning

confidence: 77%

“…Such Schur rings are said to be of partial spread type and satisfy an equation the group is abelian, any Schur ring of (n, r)-type for r # [2,3] and n>22 is of partial spread type (Theorem 4.10).…”

Section: Introductionmentioning

confidence: 98%

On Three-Dimensional Schur Rings Obtained from Partial Spreads

Hiramine

1997

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

“…Otherwise, such an abelian group would have some element of order -0 (mod 4), hence its Sylow 2-subgroup would be Z4. But this is impossible by theorem 3.3 of [2]. From now on, let # = 2 (n = 64).…”

Section: The Abelian Singer Groups Of the Distance-regular Digraphs Omentioning

confidence: 87%

On theG-matrices with entries and eigenvalues inQ(i)

Hou

1992

Graphs and Combinatorics

View full text Add to dashboard Cite

Abstract. Let G be a finite abelian group, K a subfield of C, C[G] regarded as an algebra of matrices. ~1~ = {A e C [C]L all the entries and eigenvalues of A are in K} is an association algebra over K. In this paper, the association scheme of .d~ is determined and in the case K = Q(i), the first eigenmatrix of the association scheme computed. As an application, it is proved that Z4 x Z4 • Z4 is the only abelian group admitted as a Singer group by some distance-regular digraph of girth 4 on 64 vertices.

show abstract

“…Remark 1.5. In connection with Problem 1.3 we mention that Bridge and Mena [4] give a criterion on Cayley graphs over abelian groups with integral eigenvalues which is obtained from a group action.…”

Section: Introductionmentioning

confidence: 99%