On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings.
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Jürgen Ritter, Sudarshan K. Sehgal (1983)
Mathematische Annalen
Chen, Huanyin, Chen, Miaosen (2003)
International Journal of Mathematics and Mathematical Sciences
Todor Zh. Mollov, Nako A. Nachev (2005)
Czechoslovak Mathematical Journal
Let be an abelian group, a commutative ring of prime characteristic with identity and a commutative twisted group ring of over . Suppose is a fixed prime, and are the -components of and of the unit group of , respectively. Let be the multiplicative group of and let be the -th Ulm-Kaplansky invariant of where is any ordinal. In the paper the invariants , , are calculated, provided . Further, a commutative ring with identity of prime characteristic is said...
Segev, Yoav (1999)
Annals of Mathematics. Second Series
Jan Krempa (2001)
Colloquium Mathematicae
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 keep the arguments...
Jan Krempa (2003)
Colloquium Mathematicae
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
G. Karpilovsky (1984)
Colloquium Mathematicae
Evgenii L. Bashkirov (2008)
Commentationes Mathematicae Universitatis Carolinae
Let be an associative ring with 1 and the multiplicative group of invertible elements of . In the paper, subgroups of which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.
Danchev, Peter V. (2008)
Acta Universitatis Apulensis. Mathematics - Informatics
Dishari Chaudhuri, Anupam Saikia (2017)
Czechoslovak Mathematical Journal
Let be a finite group , a field of characteristic and let be the group of units in . We show that if the derived length of does not exceed , then must be abelian.
M.S. Raghunathan (1987/1988)
Mathematische Annalen
Czesław Bagiński (1999)
Colloquium Mathematicae
Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
Meena Sahai (1998)
Publicacions Matemàtiques
In this paper, we study the situation as to when the unit group U(KG) of a group algebra KG equals K*G(1 + J(KG)), where K is a field of characteristic p > 0 and G is a finite group.
A. A. Bovdi, A. StrojnowskI (1990)
Banach Center Publications
Rajendra K. Sharma, Gaurav Mittal (2022)
Mathematica Bohemica
We give the characterization of the unit group of , where is a finite field with elements for prime and denotes the special linear group of matrices having determinant over the cyclic group .
Gaurav Mittal, Rajendra Kumar Sharma (2021)
Mathematica Bohemica
We characterize the unit group of semisimple group algebras of some non-metabelian groups, where is a field with elements for prime and a positive integer . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.
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