122 research outputs found
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
Linear spaces with significant characteristic prime
Let be a group with socle a simple group of Lie type defined over the
finite field with elements where is a power of the prime . Suppose
that acts transitively upon the lines of a linear space . We
show that if is {\it significant} then acts flag-transitively on
and all examples are known.Comment: 11 page
Criteria for solvable radical membership via p-elements
Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable
radical of a finite group can be characterized as the set of all
such that is solvable for all $y\in G$. We prove two generalizations of
this result. Firstly, it is enough to check the solvability of for
every -element for every odd prime . Secondly, if has odd
order, then it is enough to check the solvability of for every
2-element .Comment: 17 page
Almost simple groups as flag-transitive automorphism groups of 2-designs with {\lambda} = 2
In this article, we study -designs with admitting a
flag-transitive almost simple automorphism group with socle a finite simple
exceptional group of Lie type, and we prove that such a -design does not
exist. In conclusion, we present a classification of -designs with
admitting flag-transitive and point-primitive automorphism groups
of almost simple type, which states that such a -design belongs to an
infinite family of -designs with parameter set and
for some , or it is isomorphic to the -design with
parameter set , , , , ,
, , , or
Antipodal Distance Transitive Covers of Complete Graphs
AbstractA distance-transitive antipodal cover of a complete graphKnpossesses an automorphism group that acts 2-transitively on the fibres. The classification of finite simple groups implies a classification of finite 2-transitive permutation groups, and this allows us to determine all possibilities for such a graph. Several new infinite families of distance-transitive graphs are constructed
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