We consider a uniform model of computation for groups. This is a generalization of the Blum Shub Smale model over the additive group of real numbers. We show that the inequalities P{DNP and PQ{DNPQ hold for computations with or without parameters over arbitrary infinite abelian groups.
On the isomorphism problem for just-infinite groups
β Scribed by Robert C. Brigham
- Publisher
- John Wiley and Sons
- Year
- 1971
- Tongue
- English
- Weight
- 414 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T β G, Cay(G, S) βΌ = Cay(G, T ) implies S Ξ± = T for some Ξ± β 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;
For a subset S of a group G such that 1 / β 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 β S. Each Ο β Aut(G) induces an isomorphism from Cay(G, S) to the Cayley graph Cay(G, S Ο ). For a positive integer m, th
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