Abstract
Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer module characters. Based on Isaacss work, we introduce the definition of Mπ-groups, and prove that if G=NwrCp is an Mπ-group, where Cp is a cyclic group of order p and pπ, then N is an Mπ-group.
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