The groups with order p7 for odd prime p - O'Brien, E; Vaughan-Lee, MR (2005)
We determine product presentations for the nilpotent Lie rings with order p7 where p ≥ 7 is prime, and then use the Baker-Campbell-Hausdorff formula to construct power-commutator presentations for the corresponding groups. The number of such groups is a polynomial depending on p whose leading term is 3p5. We complete the determination of groups with order p7 for p = 3, 5 using the p-group generation algorithm. We provide access to the resulting presentations for the groups via a database distributed with computer algebra systems. © 2005 Elsevier Inc. All rights reserved.