Displaying similar documents to “On free subgroups of units in quaternion algebras II”

On free subgroups of units in quaternion algebras

Jan Krempa (2001)

Colloquium Mathematicae

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It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to...

Units in group rings of crystallographic groups

Karel Dekimpe (2003)

Fundamenta Mathematicae

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In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the...

A Note on Additive Groups of Some Specific Associative Rings

Mateusz Woronowicz (2016)

Annales Mathematicae Silesianae

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Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.

A class of quasitilted rings that are not tilted

Riccardo Colpi, Kent R. Fuller, Enrico Gregorio (2006)

Colloquium Mathematicae

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Based on the work of D. Happel, I. Reiten and S. Smalø on quasitilted artin algebras, the first two authors recently introduced the notion of quasitilted rings. Various authors have presented examples of quasitilted artin algebras that are not tilted. Here we present a class of right quasitilted rings that not right tilted, and we show that they satisfy a condition that would force a quasitilted artin algebra to be tilted.

Structure of the unit group of the group algebras of non-metabelian groups of order 128

Navamanirajan Abhilash, Elumalai Nandakumar, Rajendra K. Sharma, Gaurav Mittal (2025)

Mathematica Bohemica

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We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.

Isometries between groups of invertible elements in C*-algebras

Osamu Hatori, Keiichi Watanabe (2012)

Studia Mathematica

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We describe all surjective isometries between open subgroups of the groups of invertible elements in unital C*-algebras. As a consequence the two C*-algebras are Jordan *-isomorphic if and only if the groups of invertible elements in those C*-algebras are isometric as metric spaces.

Pere Menal i Brufal, 1951-1991.

Joaquim Bruna, Warren Dicks (1992)

Publicacions Matemàtiques

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Pere Menal, Professor of Algebra at the Universitat Autònoma de Barcelona, died in a traffic accident on April 4th, 1991. His colleagues in the Mathematics Department of the UAB strongly felt the need to pay a tribute to his memory, and decided then to dedicate this, the Autumn 1992 issue of the departmental journal, to his memory.

Non-transitive generalizations of subdirect products of linearly ordered rings

Jiří Rachůnek, Dana Šalounová (2003)

Czechoslovak Mathematical Journal

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Weakly associative lattice rings (wal-rings) are non-transitive generalizations of lattice ordered rings (l-rings). As is known, the class of l-rings which are subdirect products of linearly ordered rings (i.e. the class of f-rings) plays an important role in the theory of l-rings. In the paper, the classes of wal-rings representable as subdirect products of to-rings and ao-rings (both being non-transitive generalizations of the class of f-rings) are characterized and the class of wal-rings...