Let Β΅ I denote the minimal number of generators of an ideal I of a local ring R M . The Dilworth number d R = max Β΅ I I an ideal of R and Sperner number sp R = max Β΅ M i i β₯ 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
An Elementary Abelian Group of Rank 4 Is a CI-Group
β Scribed by M. Hirasaka; M. Muzychuk
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 212 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
β¦ Synopsis
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 .
π SIMILAR VOLUMES
Let F be a free group of rank n. Denote by Out F its outer automorphism n n group, that is, its automorphism group modulo its inner automorphism group. For arbitrary n, by considering group actions on finite connected graphs, we derived the maximum order of finite abelian subgroups in Out F . Moreov
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
## Abstract In Β§ l of this article, we study groupβtheoretical properties of some automorphism group Ξ¨^\*^ of the metaβabelian quotient Β§ of a free proβ__l__ group Β§ of rank two, and show that the conjugacy class of some element of order two of Ξ¨^\*^ is not determined by the action induced on the a