J. Aust. Math. Soc.
78 (2005), 291295

Elements of prime power order and their conjugacy classes in finite groups

László Héthelyi
Department of Algebra
Technical University of Budapest
H1521 Budapest
Hungary
hethelyi@math.bme.hu





Abstract

We show that, for any positive integer , there are only finitely many finite groups, up
to isomorphism, with exactly conjugacy classes of elements of prime power
order. This generalizes a result of E. Landau
from 1903. The proof of our generalization makes
use of the classification of finite simple
groups.

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