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Small intersections of principal blocks. (English) Zbl 1401.20018
Summary: In this note, it is shown that a finite group \(G\) is solvable if for each odd prime divisor \(p\) of \(| G |\), \(| \operatorname{Irr}(B_0(G)_2) \cap \operatorname{Irr}(B_0(G)_p) | \leq 2\), where \(\operatorname{Irr}(B_0(G)_p)\) is the set of complex irreducible characters of the principal \(p\)-block \(B_0(G)_p\) of \(G\). Also, the structure of such groups is investigated. Examples show that the bound 2 is best possible.

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