Abstract
Let π be a set of primes and G a π -separable group. Isaacs defines the B π characters, which can be viewed as the `` π -modular'' characters in G , such that the B p' characters form a set of canonical lifts for the p -modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p -blocks to the π -blocks of a finite π -separable group, generalizing Brauer's three main theorems to the π -blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π -blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the First Main Theorem for π-blocks.
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