On units of group rings
نویسندگان
چکیده
منابع مشابه
The Units of Group-rings
when addition and multiplication are defined in the obvious way, form a ring, the group-ring of G over K, which will be denoted by R (G, K). Henceforward, we suppose that K has the modulus 1, and we denote the identity in G by e0. Then R(G,K) has the modulus l.e0. Since no confusion can arise thereby, the element 1. e in R(G, K) will be written as e, and whenever it is convenient, the elements ...
متن کاملOn the Torsion Units of Some Integral Group Rings∗
It is shown that any torsion unit of the integral group ring ZG of a finite group G is rationally conjugate to a trivial unit if G = P o A with P a normal Sylow p-subgroup of G and A an abelian p′-group (thus confirming a conjecture of Zassenhaus for this particular class of groups). The proof is an application of a fundamental result of Weiss. It is also shown that the Zassenhaus conjecture ho...
متن کاملArithmetic Rigidity and Units in Group Rings
For any finite group G the group U(Z[G]) of units in the integral group ring Z[G] is an arithmetic group in a reductive algebraic group, namely the Zariski closure of SL1(Q[G]). In particular, the isomorphism type of the Q-algebra Q[G] determines the commensurability class of U(Z[G]); we show that, to a large extent, the converse is true. In fact, subject to a certain restriction on the Q-repre...
متن کاملSome Results on Hypercentral Units in Integral Group Rings
In this note we investigate the hypercentral units in integral group rings ZG, where G is not necessarily torsion. One of the main results obtained is the following (Theorem 3.5): if the set of torsion elements of G is a subgroup T of G and if Z2(U) is not contained in CU (T ), then T is either an Abelian group of exponent 4 or a Q∗ group. This extends our earlier result on torsion group rings.
متن کاملTwisted Group Rings Whose Units Form an Fc-group
Let U(KλG) be the group of units of an infinite twisted group algebra KλG over a field K. We describe the maximal FC-subgroup of U(KλG) and give a characterization of U(KλG) with finitely conjugacy classes. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus’ theorem.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1980
ISSN: 0022-4049
DOI: 10.1016/0022-4049(80)90028-6