Results 171 to 180 of about 816 (210)

The pseudorational rank of an abelian group [PDF]

Siberian Mathematical Journal, 2005
We study finite-rank torsion-free abelian groups and quotient divisible mixed groups. We consider the pseudorational rank, a new invariant for finite-rank torsion-free groups which was introduced by A. A. Fomin, and establish its connection with the usual rank.
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POWER GROUPS OF FREE ABELIAN GROUPS OF FINITE RANK [PDF]

Communications in Algebra, 2002
ABSTRACT The power set of a group G has an induced semigroup structure, some subsets of which will form groups in their own right. We are especially interested in such subsets that are maximal. We demonstrate that even when G is a free abelian group of finite rank, the groups which arise in this way can be diverse profinite abelian groups.
Geoff C. Smith, Gunnar Traustason
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Minimal rank of abelian group matrices

Linear and Multilinear Algebra, 1998
The minimal rank of abelian group matrices with positive integral entries is determined.The corresponding problem for circulant matrices have been investigated by Ingleton and more recently by Shiu-Ma-Fang. Our work can be viewed as a generalization of their results, since a group matrix becomes circulant when the group is cyclic.
Wai Kiu Chan, Yip-Cheung Chan, Man-Keung Siu   +2 more
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The rank of a latin square associated to an abelian group

Communications in Algebra, 2000
Let be a finite abelian group, where pi (1 ≤ i ≤ r) are (not necessarily distinct) odd primes. Suppose . Using a result of Carlitz and Moser, we show that . Consequently, we prove that the rank of any Latin square associated with the group G is at least . This sharpens a result in [2].
Leung, K.H., Ling, S.
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On Hyper (Abelian of Finite Rank) Groups

Algebra Colloquium, 2008
We study the class of groups G, each of whose non-trivial images contains a non-trivial abelian normal subgroup of finite rank. This is very much wider than the class, studied earlier by Robinson and others, of hyperabelian groups H with finite abelian section rank. Our main results are that these groups G are hypercentral by residually finite and are
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Covering Groups of Rank 1 of Elementary Abelian Groups

Communications in Algebra, 2006
ABSTRACT Covering groups of elementary Abelian groups of odd exponent p can be classified according to the rank of their pth power homomorphisms, which may be regarded as linear transformations of  p –vector spaces. This article contains a description of the isomorphism types and the automorphism groups of those covering groups in which this rank is 1.
Rachel Quinlan, Rod Gow
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The rank of abelian groups with commutative endomorphism ring

Communications in Algebra, 2020
AbstractThis paper compares of the rank of a torsion-free Abelian group G of finite rank and the rank of its endomorphism ring E(G) under the condition that E(G) is commutative.
Ulrich Albrecht, Pat Goeters, H. Huang
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Abelian automorphism groups of countable rank

1999
The abelian automorphism groups of countable rank are largely determined. Those arising from automorphisms of torsion-free groups are completely determined.
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The nice basis rank of a primary abelian group

Studia Scientiarum Mathematicarum Hungarica, 2011
An abelian p-group G has a nice basis if it is the ascending union of a sequence of nice subgroups, each of which is a direct sum of cyclic groups. It is shown that if G is any group, then G ⊕ D has a nice basis, where D is the divisible hull of pωG. This leads to a consideration of the nice basis rank of G, i.e., the smallest rank of a divisible group
Patrick W. Keef, Peter V. Danchev
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