Results 1 to 10 of about 2,784,512 (232)
The dp-rank of abelian groups [PDF]
J. symb. log. 84 (2019) 957-986, 2017 An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik-Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups $A$ such that there is only finitely many primes $p$ such that the ...
Yatir Halevi, D. Palacín
arxiv +9 more sources
Faithful abelian groups of infinite rank [PDF]
Proceedings of the American Mathematical Society, 1988 Let B B be a subgroup of an abelian group G G such that G / B G/B is isomorphic to a direct sum of copies of an abelian group A A . For B B to be a direct summand of G G , it is necessary that G ...
Ulrich Albrecht
+5 more sources
On the Prüfer rank of mutually permutable products of abelian groups [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2018 The first and third authors are supported by the Grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. The first and fourth authors are supported by Prometeo/2017/057 of Generalitat, Valencian Community, Spain.
A. Ballester-Bolinches +3 more
semanticscholar +2 more sources
An Elementary Abelian Group of Rank 4 Is a CI-Group
Journal of Combinatorial Theory, Series A, 2001 AbstractIn this paper we prove that Z4p is a CI-group; i.e., two Cayley graphs over the elementary abelian group Z4p are isomorphic if and only if their connecting sets are conjugate by an automorphism of the group Z4p.
Mitsugu Hirasaka, Mikhail Muzychuk
openalex +2 more sources
An elementary abelian group of large rank is not a CI-group
Discrete Mathematics, 2003 AbstractIn this paper, we prove that the group Zpn is not a CI-group if n⩾2p−1+(2p−1p), that is there exist two Cayley digraphs over Zpn which are isomorphic but their connection sets are not conjugate by an automorphism of Zpn.
Mikhail Muzychuk
openalex +3 more sources
Acentralizers of Abelian groups of rank 2
Hacettepe Journal of Mathematics and Statistics, 2019 Let $G$ be a group. The Acentralizer of an automorphism $\alpha$ of $G$, is the subgroup of fixed points of $\alpha$, i.e., $C_G(\alpha)= \{g\in G \mid \alpha(g)=g\}$. We show that if $G$ is a finite Abelian $p$-group of rank $2$, where $p$ is an odd prime, then the number of Acentralizers of $G$ is exactly the number of subgroups of $G$.
Zahar MOZAFAR, Bijan Taerı
openalex +5 more sources
Cartan actions of higher rank abelian groups and their classification
Journal of the American Mathematical Society, 2023 We study R k × Z ℓ \mathbb {R}^k \times \mathbb {Z}^\ell actions on arbitrary compact manifolds with a projectively dense set of Anosov elements and 1-dimensional coarse Lyapunov foliations.
Ralf Spatzier, Kurt Vinhage
openalex +3 more sources
Strong ordered Abelian groups and dp-rank [PDF]
arXiv, 2017 We provide an algebraic characterization of strong ordered Abelian groups: An ordered Abelian group is strong iff it has bounded regular rank and almost finite dimension. Moreover, we show that any strong ordered Abelian group has finite Dp-rank. We also provide a formula that computes the exact valued of the Dp-rank of any ordered Abelian group.
arxiv +3 more sources
The typeset and cotypeset of a rank 2 abelian group [PDF]
Pacific Journal of Mathematics, 1978 Phillip Schultz
openalex +4 more sources
On the splitting of rank one Abelian groups
Journal of Algebra, 1971 A. E. Stratton
openalex +3 more sources