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Original Articles

On a Class of Non-commutative Imprimitive Association Schemes of Rank 6

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Pages 4008-4041 | Received 20 Feb 2014, Published online: 26 Jun 2015
 

Abstract

Many facts about group theory can be generalized to the context of the theory of association schemes. In particular, association schemes with fewer than 6 elements are all commutative. While there is a nonabelian group with 6 elements which is unique up to isomorphism, there are infinitely many isomorphism classes of non-commutative association schemes with 6 elements. All examples previously known to us are imprimitive, and fall into three classes which are reasonably well understood. In this paper, we construct a fourth class of noncommutative, imprimitive association schemes of rank 6.

2010 Mathematics Subject Classification:

Notes

The authors thank the anonymous referee for pointing out to them that this idea, which we found in [Citation6], originally appeared in Schur's proof of Burnside's Theorem.

Communicated by S. Sehgal.

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