J. Aust. Math. Soc.
77 (2004), 387-400
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Certain relations between p-regular class sizes and the
p-structure of
p-solvable groups
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Antonio Beltrán
Departamento de Matemáticas
Universidad Jaume I
Castellón 12071
Spain
abeltran@mat.uji.es
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María José Felipe
Departamento de Matemática Aplicada
Universidad Politécnica de Valencia
Valencia 46022
Spain
mfelipe@mat.upv.es
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Abstract
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Let G
be a finite
p-solvable group for a fixed prime
p. We study how certain arithmetical conditions on
the set of
p-regular conjugacy class sizes of
G influence the
p-structure of
G. In particular, the structure of the
p-complements of
G is described when this set is
 for arbitrary coprime integers
 . The structure of
G is determined when the noncentral
p-regular class lengths are consecutive numbers
and when all of them are prime powers.
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