✦ LIBER ✦

Primitive Localizations of Group Algebras of Polycyclic-by-Finite Groups

✍ Scribed by P. Wauters

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 90 KB
Volume: 214
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7720

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a polycyclic-by-finite group such that ⌬ G is torsion-free abelian and K a field. Denote by S a multiplicatively closed set of non-zero central elements of w x K G ; if K is an absolute field assume that S contains an element not in K. Our w x main result is when the localization K G is a primitive ring. This turns out to be S Ž .

² y1 : Ž . equivalent to the following three conditions:

finite, condition 3 is not needed. An immediate consequence is the following. Let Ž . K be a field; in case K is an absolute field assume that ⌬ G / 1. Then w x K G is a primitive ring. In the final section a class of examples is con -

structed.

📜 SIMILAR VOLUMES

Locally (Soluble-by-Finite) Groups of Fi

Locally (Soluble-by-Finite) Groups of Finite Rank

✍ Martyn R. Dixon; Martin J. Evans; Howard Smith 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 178 KB

But P l B s rad P and so L ( Prrad P. It remains to show that P F L . 1 2 If Q is a maximal normal subgroup of P then, since P is perfect, PrQ is isomorphic to a simple direct factor of L and hence has order greater 1 than s. With the notation as in Lemma 2.2, we have PE rE ( PrP l E , 2 2 2 which t

On Primitive Linear Representations of F

On Primitive Linear Representations of Finite Groups

✍ Michael Aschbacher 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 129 KB

Primitivity of Permutation Groups, Coher

Primitivity of Permutation Groups, Coherent Algebras and Matrices

✍ Gareth A. Jones; Mikhail Klin; Yossi Moshe 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 114 KB

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give

Nil Algebras and Unipotent Groups of Fin

Nil Algebras and Unipotent Groups of Finite Width

✍ Consuelo Martı&#x0301;nez; Efim Zelmanov 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 186 KB

Locally Finite Simple Groups of 1-Type

✍ Stefaan Delcroix; Ulrich Meierfrankenfeld 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 152 KB

A locally finite, simple group G is said to be of 1-type if every Kegel cover for G has a factor which is an alternating group. In this paper we study the finite subgroups of locally finite simple groups of 1-type. We also introduce the concept of ''block-diagonal embeddings'' for groups of alternat

On the List of Finite Primitive Permutat

On the List of Finite Primitive Permutation Groups of Degree ≤ 50

✍ FRANCIS BUEKENHOUT; DIMITRI LEEMANS 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 454 KB

We complete data in Sims' list of the 406 primitive permutation groups of degree ≤ 50, as given in a CAYLEY library, by an explicit description of the structure of the 202 groups missing till now. The completed list is available in MAGMA.