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Field name	Details
Dewey Class	512.46
Title	Group Identities on Units and Symmetric Units of Group Rings ([Ebook]) / by Gregory T. Lee.
Author	Lee, Gregory T.
Other name(s)	SpringerLink (Online service)
Publication	London : Springer London , 2010.
Physical Details	XII, 196 pages : online resource.
Series	Algebra and Applications ; 12
ISBN	9781849965040
Summary Note	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.:
Contents note	Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of U(FG) and U+(FG) -- The Bounded Engel Property -- Solvability of U(FG) and U+(FG) -- Further Reading -- Some Results on Prime and Semiprime Rings.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-84996-504-0
Links to Related Works	Subject References: Algebra . Associative Rings and Algebras . Group theory . Group Theory and Generalizations . Mathematics . Authors: Lee, Gregory T. . Corporate Authors: SpringerLink (Online service) . Series: Algebra and Applications . Classification: 512.46 . 512.46 (DDC 23) .

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Group Identities on Units and Symmetric Units of Group Rings

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