Units of group rings of groups of order 16. (English) Zbl 0798.16019
Continuing work done by the first author and G. Leal [in Commun. Algebra 19, 1809-1827 (1991; Zbl 0723.16015)] an explicit description of the unit group \(U\) of the integral group rings \(\mathbb{Z} G\) for all groups \(G\) of order 16 is given. It is also shown that \(D_{16}\) is the only non-abelian indecomposable group of that order for which the group generated by the Bass-Milnor cyclic and the bicyclic units has finite index in \(U\).
Reviewer: J.Ritter (Augsburg)
MSC:
| 16U60 | Units, groups of units (associative rings and algebras) |
| 16S34 | Group rings |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
Keywords:
groups of order 16; Bass-Milnor cyclic units; unit group; integral group rings; bicyclic unitsCitations:
Zbl 0723.16015References:
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