Group Identities on Units and Symmetric Units of Group Rings - ISBN:184996503X

Group Identities on Units and Symmetric Units of Group Rings

Date: 21 April 2011, 03:34

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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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