Isomorphism-invariants and their applications in testing for isomorphism between finitely presented groups
published by Damascus University
in 2013
in
and research's language is
العربية
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Abstract in English
This paper introduces some isomorphism-invariants for groups and uses
them to test two finitely presented groups. The introduced algorithm starts with
the construction of all cyclic groups contained in the groups under test, then it
compares the distribution of a particular set of elements in the constructed
cyclic groups. The algorithm leads to one of these two results:
1. The groups have the same "fingerprint"
2. The groups are not isomorphic
References used
Holt, D. F., Bettina Eick and Eamonn A.O’Brien. (2005). Handbook of Computational Group Theory. Chapman & Hall/CRC Press
Holt, D. F. and Sarah Rees. (1992). Testing for isomorphism between finitely presented groups. Groups, Combinatorics & Geometry Durham, 1990. London Mathematical Society Lecture Note Series 165. 459-475
Magnus, W., Karrass, A. and Solitar, D. (1966). Combinatorial Group Theory Presentations of Groups in Terms of Generators and Relations. Dover Publications, INC. New York