Geometry of defining relations in groups. (English) Zbl 0732.20019

Ol’shanskij, A. Yu.

Mathematics and Its Applications. Soviet Series, 70. Dordrecht etc.: Kluwer Academic Publishers. xxvi, 505 p. Dfl. 340.00; $ 185.00; £115.00 (1991).

See the review of the Russian original (Moscow, Nauka 1989) in Zbl 0676.20014.

MSC:

20F05	Generators, relations, and presentations of groups
20-02	Research exposition (monographs, survey articles) pertaining to group theory
20F50	Periodic groups; locally finite groups
20F06	Cancellation theory of groups; application of van Kampen diagrams
20E15	Chains and lattices of subgroups, subnormal subgroups
20E34	General structure theorems for groups

Keywords:

method of graded diagrams; groups; subgroups; 2-dimensional topology; diagrams over groups; periodic groups; defining relations