Some remarks on Sylow subgroups of general linear groups (Q1071870)

The authors give a detailed description of the maximal p-subgroups of GL(n,F) for any prime p and any field F. \textit{R. T. Vol'vachev} [in Izv. Akad. Nauk SSSR, Ser. Mat. 27, 1031-1054 (1963; Zbl 0132.275), \(=Am\). Math. Soc., Transl., II. Ser. 64, 216-243 (1967)], claimed to do this, but his list omitted some cases when \(p=2\) over certain fields of characteristic zero, for example over the field of 2-adic numbers. For some fields of characteristic zero the maximal 2-subgroups of GL(n,F) are not all conjugate, as claimed by Vol'vachev. The authors' description of the maximal 2-subgroups in these cases involve a certain field invariant, which in practice may not be easy to compute. The authors compute this invariant for very many interesting fields.