Connection between irreducible representations of a finite p-group and its associated Lie algebra (Q1091465)

It is proved that the set of degrees of irreducible complex representations of any finite metabelian p-group of exponent p and of class \(c<p\) coincides with the set of absolutely irreducible representations over GF(p) of the associated Lie algebra of this group. The same coincidence is proved for the free n-generator group of exponent p and of class \(c<p\) and the free n-generator nilpotent of class c Lie algebra over GF(p). Both results are corollaries of a technical theorem which gives further information on the categorical isomorphism between the category of Lie algebras over GF(p) which are nilpotent of class \(c<p\) and the category of p-groups of exponent p which are nilpotent of class \(c<p\) (the isomorphism is given by a Campbell-Hausdorff formula).