An Extension Theorem for Terraces

  • Matt Ollis
  • Devin Willmott
Keywords: 2-sequencing, Bailey's conjecture, extendable terrace, rotational terrace, terrace.


We generalise an extension theorem for terraces for abelian groups to apply to non-abelian groups with a central subgroup isomorphic to the Klein 4-group $V$.  We also give terraces for three of the non-abelian groups of order a multiple of 8 that have a cyclic subgroup of index 2 that may be used in the extension theorem.  These results imply the existence of terraces for many groups that were not previously known to be terraced, including 27 non-abelian groups of order 64 and all groups of the form $V^s \times D_{8k}$ for all $s$ and all $k > 1$ where $D_{8k}$ is the dihedral group of order $8k$.  

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