Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T โ G, Cay(G, S) โผ = Cay(G, T ) implies S ฮฑ = T for some ฮฑ โ Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property;
On the Complexity of the Isomorphism Relation for Finitely Generated Groups
โ Scribed by Simon Thomas; Boban Velickovic
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 158 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For a positive integer m, a group G is said to have the m-DCI property if, for any Cayley digraphs Cay(G, S) and Cay(G, T ) of G of valency m (that is, |S| = |T | =m), Cay(G, S)$Cay(G, T ) if and only if S \_ =T for some \_ # Aut(G). This paper is one of a series of papers towards characterizing fin
The work for this paper was carried out partly at the Courant Institute of Mathematical Sciences under NSF Grant GP-12024. Reproduction in whole or in part is permitted for any purpose of the United States Government. Communicated through G. Baumslag.
For a subset S of a group G such that 1 / โ S and S = S -1 , the associated Cayley graph Cay(G, S) is the graph with vertex set G such that {x, y} is an edge if and only if yx -1 โ S. Each ฯ โ Aut(G) induces an isomorphism from Cay(G, S) to the Cayley graph Cay(G, S ฯ ). For a positive integer m, th
We prove that the analog of the Grushko-Neumann theorem does not hold for profinite free products of profinite groups. To do that we bound the number of generators of a finite group generated by a family of subgroups of pairwise coprime orders.