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On invertible terraces for non‐abelian groups

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 24k + 4 and 24k + 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 12k + 2 or 12k + 10; (ii) a generalized dicyclic group of order 24k + 4 or 24k + 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