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Isomorphisms of Cayley digraphs of Abelian groups
| Content Provider | Scilit |
|---|---|
| Author | Li, Cai Heng |
| Copyright Year | 1998 |
| Description | For a finite group G and a subset S of G with 1 ∉ S, the Cayley graph Cay(G, S) is the digraph with vertex set G such that (x, y) is an arc if and only if $yx^{−1}$ ∈ S. The Cayley graph Cay(G, S) is called a CI-graph if, for any T ⊂ G, whenever Cay (G, S) ≅ Cay(G, T) there is an element a σ ∈ Aut(G) such that $S^{σ}$ = T. For a positive integer m, G is called an m-DCI-group if all Cayley graphs of G of valency at most m are CI-graphs; G is called a connected m-DCI-group if all connected Cayley graphs of G of valency at most m are CI-graphs. The problem of determining Abelian m-DCI-groups is a long-standing open problem. It is known from previous work that all Abelian m-DCI-groups lie in an explicitly determined class of Abelian groups. First we reduce the problem of determining Abelian m-DCI-groups to the problem of determining whether every subgroup of a member of is a connected m-DCI-group. Then (for a finite group G, letting p be the least prime divisor of |G|,) we completely classify Abelian connected (p + 1)-DCI-groups G, and as a corollary, we completely classify Abelian m-DCI-groups G for m ≤ p + 1. This gives many earlier results when p = 2. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1F715564A78568EF7B0CDCB386D0B6A3/S0004972700031579a.pdf/div-class-title-isomorphisms-of-cayley-digraphs-of-abelian-groups-div.pdf |
| Ending Page | 188 |
| Page Count | 8 |
| Starting Page | 181 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700031579 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 2 |
| Volume Number | 57 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1998-04-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Finite Group Abelian Groups Cayley Graphs |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
