✦ LIBER ✦

On invertible terraces for non-abelian groups

✍ Scribed by M. A. Ollis; Roger M. Whitaker

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 159 KB
Volume: 15
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20127

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✦ Synopsis

Abstract

We give several constructions for invertible terraces and invertible directed terraces. These enable us to give the first known infinite families of invertible terrraces, both directed and undirected, for non‐abelian groups. In particular, we show that all generalized dicyclic groups of orders 24__k__ + 4 and 24__k__ + 20 have an invertible directed terrace and that all groups of the form A × G have an invertible terrace, where A is an (possibly trivial) abelian group of odd order and G is any one of: (i) a generalized dihedral group of order 12__k__ + 2 or 12__k__ + 10; (ii) a generalized dicyclic group of order 24__k__ + 4 or 24__k__ + 20; (iii) a non‐abelian group of order n with 10 ≤ n ≤ 21; (iv) a non‐abelian binary group of order n with 24 ≤ n ≤ 42. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 437–447, 2007

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