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Prime powers as conjugacy class lengths of π-elements

Published online by Cambridge University Press:  17 April 2009

Antonio Beltrán  and
María José Felipe
Antonio Beltrán
Affiliation:
Departamento de Matemáticas, Universidad Jaume, I 12071 CastellóSpain e-mail: abeltran@mat.uji.es
María José Felipe
Affiliation:
Departamento de Matemática Aplicada, Universided Politécnica de Valencia, 46022 ValenciaSpain e-mail: mfelipe@mat.upv.es
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Let G be a finite group and π an arbitrary set of primes. We investigate the structure of G when the lengths of the conjugacy classes of its π-elements are prime powers. Under this condition, we show that such lengths are either powers of just one prime or exactly {1,qa, rb}, with q and r two distinct primes lying in π and a, b > 0. In the first case, we obtain certain properties of the normal structure of G, and in the second one, we provide a characterisation of the structure of G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 317 - 325
Copyright
Copyright © Australian Mathematical Society 2004

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