Group isomorphism problem: Difference between revisions
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In [[abstract algebra]], the '''group isomorphism problem''' is the [[decision problem]] of determining whether two [[Presentation of a group|group presentation]]s present [[Isomorphism|isomorphic]] [[Group (mathematics)|group]]s. | In [[abstract algebra]], the '''group isomorphism problem''' is the [[decision problem]] of determining whether two [[Presentation of a group|group presentation]]s present [[Isomorphism|isomorphic]] [[Group (mathematics)|group]]s. | ||
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==References== | ==References== | ||
* {{cite book | * {{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 = [[Mathematische Annalen|Math. Ann.]] | volume = 71 | issue = | pages = 116-144 | publisher = | location = | date = 1911 | url = | doi = 10.1007/BF01456932 | id = | accessdate = }} | |||
| pages = 24 | |||
| doi = | |||
| id = | |||
| isbn = 0-486-63281-4}} | |||
* {{cite book | |||
| coauthors = | |||
| title = Presentations of groups | |||
| pages = 49 | |||
| doi = | |||
| id = | |||
| isbn = 0-521-37203-8}} | |||
* {{cite journal | |||
| title = Über unendliche diskontinuierliche Gruppen | |||
| pages = 116-144 | |||
| location = | |||
| date = 1911 | |||
| doi = 10.1007/BF01456932 | |||
| accessdate = | |||
Revision as of 16:17, 28 October 2008
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.
References
- Magnus, Wilhelm; Abraham Karrass, Donald Solitar (1976). Combinatorial group theory. Presentations of groups in terms of generators and relations. Dover Publications, 24. ISBN 0-486-63281-4.
- Johnson, D.L. (1990). Presentations of groups. Cambridge University Press, 49. ISBN 0-521-37203-8.
- Dehn, Max (1911). "Über unendliche diskontinuierliche Gruppen". Math. Ann. 71: 116-144. DOI:10.1007/BF01456932. Research Blogging.