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The parallel complexity of some constructions in combinatorial group theory. (English) Zbl 0698.68053
Summary: The parallel complexity of several important constructions in combinatorial group theory is studied. direct and free products, special HNN-extensions, extensions by finite groups, and wreath products are investigated. $$NC^ 1$$-equivalences between the complexity of the result on the one hand and the complexity of the elements of these constructions on the other hand are proved.

##### MSC:
 68Q25 Analysis of algorithms and problem complexity 20F05 Generators, relations, and presentations of groups 20D60 Arithmetic and combinatorial problems involving abstract finite groups 68W30 Symbolic computation and algebraic computation