Bailey’s Conjecture Holds Through $87$ Except Possibly for $64$

Abstract

R.A. Bailey has conjectured that all finite groups except elementary Abelian $2$-groups with more than one factor have $2$-sequencings (i.e., terraces). She verified this for all groups of order $n$, $n\le 9$. Results proved since the appearance of Bailey’s paper make it possible to raise this bound to $n\le 87$ with $n=64$ omitted. Relatively few groups of order not $2^n$, $n\in \{4,5\}$ must be handled by machine computation.