On the Lower Bound of the Derived Length of the Unit Group of a Nontorsion Group Algebra
| Autor: | Ernesto Spinelli, Sudarshan K. Sehgal, Gregory T. Lee, Tibor Juhász |
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| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
010102 general mathematics 0211 other engineering and technologies Derived length 021107 urban & regional planning Field (mathematics) 02 engineering and technology Group algebra group ring unit group 01 natural sciences Upper and lower bounds Prime (order theory) Unit group Combinatorics 0101 mathematics Nilpotent group Group ring Mathematics |
| Zdroj: | Algebras and Representation Theory. 23:457-466 |
| ISSN: | 1572-9079 1386-923X |
| DOI: | 10.1007/s10468-019-09855-x |
| Popis: | Let G be a nonabelian nilpotent group and F a field of characteristic p > 2, such that the unit group \(\mathcal {U}(FG)\) of the group ring FG is solvable and G contains a p-element. Here we provide a lower bound for the derived length of \(\mathcal {U}(FG)\) that corrects the result from Lee et al. (Algebr. Represent. Theory 17, 1597–1601 2014) when G is nontorsion and \(G^{\prime }\) is a finite p-group. |
| Databáze: | OpenAIRE |
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