The isomorphism problem for Cayley ternary relational structures for some abelian groups of order 8p
A ternary relational structure X is an ordered pair (V,E) where V is a set and E a set of ordered 3-tuples whose coordinates are chosen from V (so a ternary relational structure is a natural generalization of a 3-uniform hypergraph). A ternary relational structure is called a Cayley ternary relation...
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| Veröffentlicht in: | Discrete mathematics 2010-11, Vol.310 (21), p.2895-2909 |
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| container_title | Discrete mathematics |
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| creator | DOBSON, Edward |
| description | A ternary relational structure X is an ordered pair (V,E) where V is a set and E a set of ordered 3-tuples whose coordinates are chosen from V (so a ternary relational structure is a natural generalization of a 3-uniform hypergraph). A ternary relational structure is called a Cayley ternary relational structure of a group G if [inline image], the automorphism group of X, contains the left regular representation of G. We prove that two Cayley ternary relational structures of [inline image], p>=11 a prime, are isomorphic if and only if they are isomorphic by a group automorphism of [inline image]. This result then implies that any two Cayley digraphs of [inline image] are isomorphic if and only if they are isomorphic by a group automorphism of [inline image], p>=11 a prime. |
| doi_str_mv | 10.1016/j.disc.2010.06.032 |
| format | Article |
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A ternary relational structure is called a Cayley ternary relational structure of a group G if [inline image], the automorphism group of X, contains the left regular representation of G. We prove that two Cayley ternary relational structures of [inline image], p>=11 a prime, are isomorphic if and only if they are isomorphic by a group automorphism of [inline image]. This result then implies that any two Cayley digraphs of [inline image] are isomorphic if and only if they are isomorphic by a group automorphism of [inline image], p>=11 a prime.</description><identifier>ISSN: 0012-365X</identifier><identifier>EISSN: 1872-681X</identifier><identifier>DOI: 10.1016/j.disc.2010.06.032</identifier><identifier>CODEN: DSMHA4</identifier><language>eng</language><publisher>Kidlington: Elsevier</publisher><subject>Algebra ; Automorphisms ; Combinatorics ; Combinatorics. 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A ternary relational structure is called a Cayley ternary relational structure of a group G if [inline image], the automorphism group of X, contains the left regular representation of G. We prove that two Cayley ternary relational structures of [inline image], p>=11 a prime, are isomorphic if and only if they are isomorphic by a group automorphism of [inline image]. This result then implies that any two Cayley digraphs of [inline image] are isomorphic if and only if they are isomorphic by a group automorphism of [inline image], p>=11 a prime.</abstract><cop>Kidlington</cop><pub>Elsevier</pub><doi>10.1016/j.disc.2010.06.032</doi><tpages>15</tpages></addata></record> |
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| subjects | Algebra Automorphisms Combinatorics Combinatorics. Ordered structures Exact sciences and technology Graph theory Group theory Group theory and generalizations Isomorphism Mathematical analysis Mathematics Order, lattices, ordered algebraic structures Representations Sciences and techniques of general use |
| title | The isomorphism problem for Cayley ternary relational structures for some abelian groups of order 8p |
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