A non-Abelian variety of groups has an undecidable elementary theory
โ Scribed by A. P. Zamyatin
- Publisher
- Springer US
- Year
- 1978
- Tongue
- English
- Weight
- 408 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0002-5232
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this paper we prove that Z 4 p is a CI-group; i.e., two Cayley graphs over the elementary abelian group Z 4 p are isomorphic if and only if their connecting sets are conjugate by an automorphism of the group Z 4 p .
This is proved by induction on 7n. For ni = 0 (\*) follows immediately from the definitions. Now take a E C,:,,, for m > 0. There is c E B,,,, such t'hat ac E pCp,n,-l + + C,,;f,l+l. There is thus a' E Cl~.flr-l with a E c + pa' + Cl,.,,f+l. By induction hypothesis a' E 6' + C,.,,, for some b' E @ B
Let ยต I denote the minimal number of generators of an ideal I of a local ring R M . The Dilworth number d R = max ยต I I an ideal of R and Sperner number sp R = max ยต M i i โฅ 0 are determined in the case that R = A G , where G = Z/pZ k is an elementary abelian p-group, A zA is a principal local ring