## Pseudocharacters on anomalous products of locally indicable groups.(English. Russian original)Zbl 1167.20304

J. Math. Sci., New York 149, No. 3, 1224-1229 (2008); translation from Fundam. Prikl. Mat. 12, No. 3, 55-64 (2006).
Summary: The question on the existence of nontrivial pseudocharacters on anomalous products of locally indicable groups is considered. Some generalizations of theorems of R. I. Grigorchuk and V. G. Bardakov on the existence of nontrivial pseudocharacters on free products with amalgamated subgroup are found. It is proved that they exist on an anomalous product $$\langle G,x\mid w=1\rangle$$, where $$G$$ is a locally indicable noncyclic group. We also prove some other propositions on the existence of nontrivial pseudocharacters on anomalous products of groups. Results on the second cohomologies of these products and their nonamenability follow from the propositions on the existence of nontrivial pseudocharacters on these groups.

### MSC:

 20C15 Ordinary representations and characters 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
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### References:

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