Abstract
The question of how certain arithmetical conditions on the lengths of the conjugacy classes of a finite group G influence the group structure has been studied by several authors with many results available. The purpose of this paper is to analyse the restrictions imposed by the lengths of the conjugacy classes of some elements of the factors of a finite group G = G 1 G 2 · · · G r , which is the product of the pairwise mutually permutable subgroups G 1, G 2, . . . , G r , on its structure. Some earlier results appear as corollaries of our main theorems.
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Communicated by J. S. Wilson.
Dedicated to Professor Hermann Heineken on his 75th birthday.
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Ballester-Bolinches, A., Cossey, J. & Li, Y. Mutually permutable products and conjugacy classes. Monatsh Math 170, 305–310 (2013). https://doi.org/10.1007/s00605-012-0411-z
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DOI: https://doi.org/10.1007/s00605-012-0411-z