Enumerating classes and characters of p-groups

Abstract

We develop general formulae for the numbers of conjugacy classes and irreducible complex characters of finite p-groups of nilpotency class less than p. This allows us to unify and generalize a number of existing enumerative results, and to obtain new such results for generalizations of relatively free p-groups of exponent p. Our main tools are the Lazard correspondence and the Kirillov orbit method.

21 pages, slightly revised version, to appear in Trans. Amer. Math. Soc

References in corpus (1)

• Representation zeta functions of compact p-adic analytic groups and arithmetic groups