Abstract
Let A be a vector space over a field F and let G be a subgroup of \(\mathrm{GL}(F,A)\). This paper gives some further linear variations of a well-known theorem due to Philip Hall. For example we prove that if F has characteristic p and B is a finite dimensional subspace of A of dimension d such that A / B is G-hypercentral, and if G has finite section p-rank r, then the upper G-hypercenter has finite codimension in A, bounded by a function of d, r only. Analogues of these results in characteristic 0 are also obtained.
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Dixon, M.R., Kurdachenko, L.A. & Subbotin, I.Y. On an analogue of a theorem of P. Hall for infinite dimensional linear groups. European Journal of Mathematics 6, 577–589 (2020). https://doi.org/10.1007/s40879-019-00334-7
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DOI: https://doi.org/10.1007/s40879-019-00334-7
Keywords
- Nearly hypercentral
- Almost hypercentral
- G-hypercentral
- Finite section p-rank
- Infinite dimensional linear group
- G-nilpotent
- Upper G-central series