On prime power order elements of general linear groups.(English)Zbl 1267.20068
Summary: We classify the absolutely irreducible subgroups \(G\leqslant\mathrm{GL}_d(q)\) which are not realizable modulo scalars over any proper subfield of \(\mathrm{GF}(q)\), which are “nearly simple”, and which contain elements of prime power order greater than \(d/3\).
MSC:
| 20G40 | Linear algebraic groups over finite fields |
| 20D05 | Finite simple groups and their classification |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20C33 | Representations of finite groups of Lie type |
Keywords:
general linear groups;absolutely irreducible subgroups;finite groups of Lie type;elements of prime power order;nearly simple groupsCite
Full Text:DOI
References:
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