Group isomorphism problem
- Group isomorphism problem
In abstract algebra, the group isomorphism problem is the decision problem of determining whether two group presentations present isomorphic groups.
The isomorphism problem was identified by Max Dehn in 1911 as one of three fundamental decision problems in group theory; the other two being the word problem and the conjugacy problem. All three problems are undecidable: there does not exist a computer algorithm that correctly solves every instance of the isomorphism problem, or of the other two problems, regardless of how much time is allowed for the algorithm to run.
References
* cite book
last = Magnus
first = Wilhelm
authorlink = Wilhelm Magnus
coauthors = Abraham Karrass, Donald Solitar
title = Combinatorial group theory. Presentations of groups in terms of generators and relations
publisher = Dover Publications
date = 1976
location =
pages = 24
url =
doi =
id =
isbn = 0-486-63281-4
* cite book
last = Johnson
first = D.L.
authorlink =
coauthors =
title = Presentations of groups
publisher = Cambridge University Press
date = 1990
location =
pages = 49
url =
doi =
id =
isbn = 0-521-37203-8
* cite journal
last = Dehn
first = Max
authorlink = Max Dehn
coauthors =
title = Über unendliche diskontinuierliche Gruppen
journal = Math. Ann.
volume = 71
issue =
pages = 116-144
publisher =
location =
date = 1911
url =
doi = 10.1007/BF01456932
id =
accessdate =
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