Results 1 to 10 of about 73,642 (235)

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 typeset and cotypeset of a rank 2 abelian group [PDF]

Pacific Journal of Mathematics, 1978
Let \(A\) be a reduced rank 2 torsion-free abelian group. Denote by \(T\) the set of types of elements of \(A\), and by \(T\mathrm{'}\) the set of types of rank 1 torsion-free factor groups of A. The author characterizes such pairs \((T,T\mathrm{'})\), and counts the number of isomorphism and quasi-isomorphism classes of rank 2 groups realizing each ...
Phillip Schultz
openalex   +5 more sources

An Elementary Abelian Group of Rank 4 Is a CI-Group

Journal of Combinatorial Theory, Series A, 2001
Finite groups are dealt with. In addition to the known notion of CI-group (i.e., group possessing the Cayley isomorphism property), the authors consider the related concept of \(\text{CI}^{(2)}\)-group. Let \(F\), \(G\) be subgroups of the symmetric (permutation) group \(\text{Sym}(X)\). We say that \(G(\supseteq F)\) is \(F\)-transjugate if \(G\) acts
Mitsugu Hirasaka, Mikhail Muzychuk
openalex   +3 more sources

An elementary abelian group of large rank is not a CI-group

Discrete Mathematics, 2003
We say that a finite group \(H\) has the Cayley isomorphy (CI) property (or, shortly, \(H\) is a CI-group) if any pair of directed Cayley graphs over \(H\) is non-isomorphic unless an isomorphism exists between the digraphs which can be induced by an automorphism of \(H\).
Mikhail Muzychuk
openalex   +4 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

On the splitting of rank one Abelian groups

Journal of Algebra, 1971
A. E. Stratton
openalex   +4 more sources

Radical groups of finite abelian subgroup rank [PDF]

Illinois Journal of Mathematics, 1972
Reinhold Baer, Hermann Heineken
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

Separating invariants for certain representations of the elementary Abelian p-groups of rank two

AIMS Mathematics
For a finite group acting linearly on a vector space, a separating set is a subset of the invariant ring that separates the orbits. In this paper, we determined explicit separating sets in the corresponding rings of invariants for four families of finite
Panpan Jia , Jizhu Nan, Yongsheng Ma
doaj   +2 more sources

A note on torsion free abelian groups of infinite rank [PDF]

Proceedings of the American Mathematical Society, 1962
James D. Reid
openalex   +3 more sources