Enumerating classes and characters of p-groups

Mathematics – Group Theory

Scientific paper

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20 pages

Scientific paper

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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