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Are there any computational problems in groups that are harder than P?
There are several well known classes of groups for which the word problem, conjugacy etc. are solvable in polynomial time (hyperbolic, automatic).
Then there are several classes of groups like ...
8
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1
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Classes of groups with polynomial time isomorphism problem
It is known that the isomorphism problem for finitely presented groups is in general undecidable. What are some classes of groups whose isomorphism problem is known to be solvable in polynomial time? (...