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Sets of -powers as conjugacy class sizes
Authors:John Cossey  Trevor Hawkes
Institution:Department of Mathematics, School of Mathematical Sciences, Australian National University, Canberra, 0200, Australia ; Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Abstract:We show that any finite set of powers of a fixed prime $p$ which includes $1$ can be the set of conjugacy class sizes of a $p$-group of nilpotency class $2$. This corresponds to a result of Isaacs for degrees of irreducible characters.

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