✦ LIBER ✦

Group Identities on Units of Group Algebras

✍ Scribed by A. Giambruno; S.K. Sehgal; A. Valenti

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 178 KB
Volume: 226
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8203

No coin nor oath required. For personal study only.

✦ Synopsis

Let U be the group of units of the group algebra FG of a group G over a field F. Suppose that either F is infinite or G has an element of infinite order. We characterize groups G so that U satisfies a group identity. Under the assumption that G modulo the torsion elements is nilpotent this gives a complete classification of such groups. For torsion groups this problem has already been settled in recent years.

📜 SIMILAR VOLUMES

On Units of Twisted Group Algebras

✍ Chia-Hsin Liu 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 110 KB

We study units of twisted group algebras. Let G be a finite group and K be a field of characteristic p > 0. Assume that K is not algebraic over a finite field. We determine when units of K t G do not contain any nonabelian free subgroup. We also discuss what will happen when G is locally finite. For

Identities on Units of Algebraic Algebra

Identities on Units of Algebraic Algebras

✍ M.A. Dokuchaev; J.Z. Gonçalves 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 95 KB

Free Unit Groups in Group Algebras

✍ J.Z Gonçalves; D.S Passman 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 235 KB

Approximate Identities for Ideals of Seg

Approximate Identities for Ideals of Segal Algebras on A Compact Group

✍ Yong Zhang 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 106 KB

We show that every closed ideal of a Segal algebra on a compact group admits a central approximate identity which has the property, called condition (U), that the induced multiplication operators converge to the identity operator uniformly on compact sets of the ideal. This result extends a known on

Unit Groups of Semisimple Group Algebras

Unit Groups of Semisimple Group Algebras of Abelianp-Groups over a Field

✍ Nako A. Nachev; Todor Zh. Mollov 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 134 KB

Let G be an abelian p-group, let K be a field of characteristic different from p, and let KG be the group algebra of G over K. In this paper we give a description Ž . Ž. of the unit group U KG of KG when i K is a field of the first kind with respect 1 Ž . to p and the first Ulm factor GrG is a direc

Nonmatrix Varieties and Nil-Generated Al

Nonmatrix Varieties and Nil-Generated Algebras Whose Units Satisfy a Group Identity

✍ Yuly Billig; David Riley; Vladimir Tasić 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 209 KB

Let R = denote the group of units of an associative algebra R over an infinite field F. We prove that if R is unitarily generated by its nilpotent elements, then R = satisfies a group identity precisely when R satisfies a nonmatrix polynomial identity. As an application, we examine the group algebra