Group Identities on Units and Symmetric Units of Group Rings (2nd...

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Group Identities on Units and Symmetric Units of Group Rings (2nd Edition)

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English | 2025 | ISBN: 303204619X | 264 Pages | PDF EPUB (True) | 18 MB

This book presents the 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. 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.

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