A non-LEA sofic group. (English) Zbl 1365.20029
Summary: We describe elementary examples of finitely presented sofic groups which are not residually amenable (and thus not initially subamenable or LEA, for short). We ask if an amalgam of two amenable groups over a finite subgroup is residually amenable and answer this positively for some special cases, including countable locally finite groups, residually nilpotent groups and others.
MSC:
| 20E26 | Residual properties and generalizations; residually finite groups |
| 20E06 | Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
| 20G25 | Linear algebraic groups over local fields and their integers |
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