منابع مشابه
Quotients of CI-Groups are CI-Groups
We show that a quotient group of a CI-group with respect to (di)graphs is a CI-group with respect to (di)graphs. In [1,2], Babai and Frankl provided strong constraints on which finite groups could be CI-groups with respect to graphs. As a tool in this program, they proved [1, Lemma 3.5] that a quotient group G/N of a CI-group G with respect to graphs is a CI-group with respect to graphs provide...
متن کاملThe CI Problem for Infinite Groups
A finite group G is a DCI-group if, whenever S and S′ are subsets of G with the Cayley graphs Cay(G,S) and Cay(G,S′) isomorphic, there exists an automorphism φ of G with φ(S) = S′. It is a CI-group if this condition holds under the restricted assumption that S = S−1. We extend these definitions to infinite groups, and make two closely-related definitions: an infinite group is a strongly (D)CIf ...
متن کاملElementary abelian p - groups of rank 2 p + 3 are not CI - groups
For every prime p > 2 we exhibit a Cayley graph on Z2p+3 p which is not a CI-graph. This proves that an elementary abelian p-group of rank greater than or equal to 2p+ 3 is not a CI-group. The proof is elementary and uses only multivariate polynomials and basic tools of linear algebra. Moreover, we apply our technique to give a uniform explanation for the recent works of Muzychuk and Spiga conc...
متن کاملSome New Groups which are not CI-groups with Respect to Graphs
A group G is a CI-group with respect to graphs if two Cayley graphs of G are isomorphic if and only if they are isomorphic by a group automorphism of G. We show that an infinite family of groups which include Dn × F3p are not CI-groups with respect to graphs, where p is prime, n 6= 10 is relatively prime to 3p, Dn is the dihedral group of order n, and F3p is the nonabelian group of order 3p.
متن کاملFurther restrictions on the structure of finite CI-groups
A group G is called a CI-group if, for any subsets S, T ⊂ G, whenever two Cayley graphs Cay(G, S) and Cay(G, T ) are isomorphic, there exists an element σ ∈ Aut(G) such that S = T . The problem of seeking finite CI-groups is a longstanding open problem in the area of Cayley graphs. This paper contributes towards a complete classification of finite CI-groups. First it is shown that the Frobenius...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2013
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-013-1400-2