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Existence of nontrivial pseudo-characters on anomalous group products. (Russian, English) Zbl 1084.20005

Vestn. Mosk. Univ., Ser. I 2004, No. 6, 24-28 (2004); translation in Mosc. Univ. Math. Bull. 59, No. 6, 24-28 (2004).
The author presents a generalization of Grigorchuk’s theorem on the existence of nontrivial pseudocharacters on groups with one relation and at least three generators. This result implies assertions on the second bounded cohomology groups of some types of groups and their nonamenability.

MSC:

20C15 Ordinary representations and characters
39B52 Functional equations for functions with more general domains and/or ranges
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
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