Groups and nilpotent Lie rings whose order is the sixth power of a prime

Newman, MichaelO'Brien, E AVaughan-Lee, M R2015-12-130021-8693http://hdl.handle.net/1885/87183We prove that there are 3p2+39p+344+24gcd(p-1,3)+11gcd (p-1,4)+2gcd(p-1,5) isomorphism types of groups and nilpotent Lie rings with order p6 for every prime p≥5. We establish the result, and power-commutator presentations for the groups, in various waysGroups and nilpotent Lie rings whose order is the sixth power of a prime200410.1016/j.jalgebra.2003.11.0122015-12-12