Enumerating classes and characters of 𝑝-groups

O’Brien, E.; Voll, C.

doi:10.1090/tran/6276

Enumerating classes and characters of $p$-groups
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by E. A. O’Brien and C. Voll PDF

Trans. Amer. Math. Soc. 367 (2015), 7775-7796 Request permission

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.

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