Results 1 to 10 of about 2,701,761 (237)

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

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 ...
Halevi, Yatir, Palacín Cruz, Daniel
arxiv   +7 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

On controllers of prime ideals in group algebras of torsion-free abelian groups of finite rank [PDF]

arXiv, 2003
In the presented paper we consider some methods of studying of prime ideals in group algebras of abelian groups of finite ...
A. V. Tushev
arxiv   +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

Elementary Abelian p-groups of rank 2p+3 are not CI-groups [PDF]

arXiv, 2009
For every prime $p > 2$ we exhibit a Cayley graph of $\mathbb{Z}_p^{2p+3}$ which is not a CI-graph. This proves that an elementary Abelian $p$-group of rank greater than or equal to $2p+3$ is not a CI-group. The proof is elementary and uses only multivariate polynomials and basic tools of linear algebra.
Gábor Somlai
arxiv   +3 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

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