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Block separations and inclusions. (English) Zbl 1185.20009
Summary: We investigate the separation of characters by blocks at different primes and the inclusions of \(q\)-blocks in \(p\)-blocks (viewed as sets of characters), and use these notions to prove results on the structure of the corresponding groups. In particular, we provide a new criterion for the nilpotence of a finite group \(G\) based on the separation by principal blocks, and we show that a condition on block unions has strong structural consequences.

20C20 Modular representations and characters
20D15 Finite nilpotent groups, \(p\)-groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
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