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

Published online by Cambridge University Press:  09 April 2009

László Héthelyi  and
Burkhard Külshammer
László Héthelyi
Affiliation:
Department of AlgebraTechnical University of BudapestH-1521 BudapestHungary e-mail: hethelyi@math.bme.hu
Burkhard Külshammer
Affiliation:
Mathematical Institute University of JenaD-07737 JenaGermany e-mail: kuelshammer@uni-jena.de
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Abstract

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We show that, for any positive integer k, there are only finitely many finite groups, up to isomorphism, with exactly k 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 2 , April 2005 , pp. 291 - 295
Copyright
Copyright © Australian Mathematical Society 2005

References

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