CONJUGATELY DENSE SUBGROUPS OF 3-DIMENSIONAL LINEAR GROUPS OVER LOCALLY FINITE FIELD

A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL 3(K) ≤ G ≤ GL 3(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in "Kourovka Notebook" for the group GL 3(K) over locally finite field K.