International Journal of Group Theory (Dec 2015)
Groups of order p^8 and exponent p
Abstract
We prove that for p>7 there are p^4 +2p^3 +20p^2 +147p+(3p+29)gcd(p−1,3)+5gcd(p−1,4)+1246 groups of order p^8 with exponent p. If P is a group of order p^8 and exponent p, and if P has class c>1 then P is a descendant of P/γ c (P). For each group of exponent p with order less than p^8 we calculate the number of descendants of order p^8 with exponent p. In all but one case we are able to obtain a complete and irredundant list of the descendants. But in the case of the three generator class two group of order p^6 and exponent p (p>3 ), while we are able to calculate the number of descendants of order p^8, we have not been able to obtain a list of the descendants.
