Fixed point free elements of prime order - School of Maths and Stats ...
Fixed point free elements of prime order - School of Maths and Stats ...
Fixed point free elements of prime order - School of Maths and Stats ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Elusive groupsWe say that a transitive permutation group is elusive if it has n<strong>of</strong>ixed <strong>point</strong> <strong>free</strong> <strong>elements</strong> <strong>of</strong> <strong>prime</strong> <strong>order</strong>.For example, M 11 acting on 12 <strong>point</strong>s.Existence <strong>of</strong> a fixed <strong>point</strong> <strong>free</strong> element <strong>of</strong> <strong>prime</strong> <strong>order</strong> is equivalentto existence <strong>of</strong> a semiregular subgroup.G is elusive on Ω if <strong>and</strong> only if every conjugacy class <strong>of</strong> <strong>elements</strong> <strong>of</strong><strong>prime</strong> <strong>order</strong> meets G ω nontrivially.