FINITE NONABELIAN p-GROUPS OF EXPONENT > p WITH A SMALL NUMBER OF MAXIMAL ABELIAN SUBGROUPS OF EXPONENT > p

Y. Berkovich has proposed to classify nonabelian finite p-groups G of exponent > p which have exactly p maximal abelian subgroups of exponent > p and this was done here in Theorem 1 for p = 2 and in Theorem 2 for p > 2. The next critical case, where G has exactly p + 1 maximal abelian subgroups of exponent > p was done only for the case p = 2 in Theorem 3.