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Generic units in abelian group rings
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Zbigniew Marciniak
Published/Copyright:
November 18, 2005
Abstract
We introduce generic units in ℤCn
and prove that they are precisely the shifted cyclotomic polynomials. They
generate the group 
of constructible units. For each cyclic group we
produce a basis of a finite index subgroup of integral units consisting of
certain irreducible cyclotomic polynomials; this extends a result of Hoechsmann
and Ritter. We also study ‘alternating-like’ units and decide when they generate
a subgroup of finite index.
:
Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
Articles in the same Issue
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
