Lee Group Identities on Units and Symmetric Units of Group Rings

1. Auflage 2010
ISBN: 978-1-84996-504-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 12, 198 Seiten

Reihe: Algebra and Applications

Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.

Autoren/Hrsg.

Lee, Gregory T

Inhaltsverzeichnis

1;Group Identities on Units and Symmetric Units of Group Rings;4
2;Preface;7
3;Contents;10
4;Chapter 1:Group Identities on Units of Group Rings;12
5;Chapter 2:Group Identities on Symmetric Units;55
6;Chapter 3:Lie Identities on Symmetric Elements;86
7;Chapter 4:Nilpotence of U(FG) and U+(FG);111
8;Chapter 5:The Bounded Engel Property;144
9;Chapter 6:Solvability of U(FG) and U+(FG);155
10;Chapter 7:Further Reading;166
11;Appendix A Some Results on Prime and Semiprime Rings;175
12;References;191
13;Index;195