An Extension Theorem for Terraces

We generalise an extension theorem for terraces for abelian groups to apply to nonabelian 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 ×D8t for all s and all t > 1 where D8t is the dihedral group of order 8t. AMS 2010 Subject Classification. Primary: 20D60. Secondary: 05B99.