Results 201 to 210 of about 2,701,761 (237)

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 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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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 Non-Slender Rank of an Abelian Group

1984
For a family (Ai)i∈I of Abelian groups and a cardinal K we define the K-product \(\mathop \Pi \limits_{i \in I} {A_i}\) to be the subgroup of the cartesian product \({\mathop \Pi \limits_I ^{(K)}}A\) consisting of all elements which support is less than K. Let us write AI(K) instead of \({A^{I(w)}} = \mathop \oplus \limits_I A\), A(I) instead of (math)
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Induced Representations of Abelian Groups of Finite Rank

Ukrainian Mathematical Journal, 2003
We prove that any irreducible faithful representation of an almost torsion-free Abelian group G of finite rank over a finitely generated field of characteristic zero is induced from an irreducible representation of a finitely generated subgroup of the group G.
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TORSION-FREE ABELIAN GROUPS OF RANK 3

Mathematics of the USSR-Sbornik, 1991
Torsion-free abelian groups similar in properties to torsion-free abelian groups of rank 3, in particular the groups of rank 3 themselves, can be characterized up to quasi-isomorphism by means of certain invariants. From the invariants of each such group one can compute invariants of its pure subgroups and invariants of its factor-groups modulo its ...
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On Blocks with Abelian Defect Groups of Small Rank

Results in Mathematics, 2016
Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p 4. Then, we show that B satisfies Brauer’s k(B)-Conjecture (i.e. $${k(B)\le|D|}$$
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