3 research outputs found
Finite projective planes admitting a projective linear group PSL (2,q)
AbstractLet S be a projective plane, and let G⩽Aut(S) and PSL(2,q)⩽G⩽PΓL(2,q) with q>3. If G acts point-transitively on S, then q=7 and S is of order 2
Large dimensional classical groups and linear spaces
Suppose that a group has socle a simple large-rank classical group.
Suppose furthermore that acts transitively on the set of lines of a linear
space . We prove that, provided has dimension at least 25,
then acts transitively on the set of flags of and hence the
action is known. For particular families of classical groups our results hold
for dimension smaller than 25.
The group theoretic methods used to prove the result (described in Section 3)
are robust and general and are likely to have wider application in the study of
almost simple groups acting on finite linear spaces.Comment: 32 pages. Version 2 has a new format that includes less repetition.
It also proves a slightly stronger result; with the addition of our
"Concluding Remarks" section the result holds for dimension at least 2