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Locally Finite Finitary Skew Linear Groups
Author(s) -
Wehrfritz B. A. F.
Publication year - 2001
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s002461150101293x
Subject(s) - finitary , mathematics , primitive permutation group , combinatorics , division ring , automorphism , vector space , group (periodic table) , mathematics subject classification , finite group , order (exchange) , discrete mathematics , symmetric group , pure mathematics , division (mathematics) , arithmetic , cyclic permutation , chemistry , organic chemistry , finance , economics
Let V be a vector space over the division ring D of infinite dimension. We study locally finite, primitive groups G of finitary linear automorphisms of V . We show that the derived group G ′ of G is infinite, simple, and lies in every non‐trivial normal subgroup of G , and that G ′ ⩽ G ⩽ Aut G ′. Moreover if char D = 0, then G is either the finitary symmetric group or the alternating group on some infinite set. If D is commutative, that is, if D is a field, then all these results are known and are the consequence of the collective work of a number of people: in particular (in alphabetical order) V. V. Belyaev, J. I. Hall, F. Leinen, U. Meierfrankenfeld, R. E. Phillips, O. Puglisi, A. Radford and quite probably others. 2000 Mathematics Subject Classification : 20H25, 20H20, 20F50.