Construction of Sylow p-subgroups of a bounded linear group (Q1109897)

Let V be a vector space with a countable base over a finite field F. Let E be the identity transformation of V. A transformation g of V is called bounded if \(\dim (g-E)V<\infty\). Such g form a group GL(V) which is called bounded (or finitary) linear group. The author indicates some constructions of Sylow p-subgroups of GL(V) for \(p=char F\) and shows that all Sylow p-subgroups can not be obtained in such a way. This is in contrast with the case \(p\neq char F\) considered earlier by \textit{I. D. Ivanyuta} [Ukr. Mat. Zh. 32, 813-818 (1980; Zbl 0466.20018)].