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\(M\)-blocks of solvable groups. (English) Zbl 0881.20005

C. Bessenrodt [J. Aust. Math. Soc., Ser. A 48, 264-280 (1990; Zbl 0703.20007)] introduced the concept of an \(M\)-block (this is a \(p\)-block in which each irreducible ordinary character is monomial), and for finite solvable groups some sufficient conditions were found for a \(p\)-block to be an \(M\)-block. The author reformulates these for odd order groups and also gives weaker conditions. Moreover, the connection between the monomiality (subnormal monomiality) of the group and the respective properties of the principal block or blocks of maximal defect are studied and several examples are provided. Sample: A finite solvable group is an \(M\)-group if every \(p\)-block of maximal defect of every subgroup is an \(M\)-block.

MSC:

20C15 Ordinary representations and characters
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20C20 Modular representations and characters

Citations:

Zbl 0703.20007
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