An upper bound for Loewy lengths of projective modules in p-solvable groups (Q1100274)
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scientific article; zbMATH DE number 4042132
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An upper bound for Loewy lengths of projective modules in p-solvable groups |
scientific article; zbMATH DE number 4042132 |
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An upper bound for Loewy lengths of projective modules in p-solvable groups (English)
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1987
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Let K be a field of prime characteristic p and let G be a finite p- solvable group. Let P be a projective indecomposable module of the group ring K(G). It is proved that the Loewy length of P is bounded by max\(\{| V|:\) V is a vertex of a composition factor of \(P\}\) and that this bound is attained if and only if P belongs to a block with cyclic defect group.
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finite p-solvable group
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projective indecomposable module
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group ring
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Loewy length
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vertex
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block
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cyclic defect group
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