Shows bounds on the index of a group related to Hall subgroups, indicating constraints for finite solvable groups.
Suppose that G is a finite solvable group and let H be a Hall π π -subgroup, let b ( H ) be the largest character degree of H , we show that |G:Oπ ' π(G)|π ≤ b(H)². | G : O π ′ π ( G ) | π ≤ b ( H ) 2 .
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Das et al. (2026) studied this question.
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