Classical Groups, Derangements And Primes (australian Mathematical Society Lecture Series)
by Timothy C. Burness /
2016 / English / PDF
2.5 MB Download
A classical theorem of Jordan states that every finite transitive
permutation group contains a derangement. This existence result has
interesting and unexpected applications in many areas of
mathematics, including graph theory, number theory and topology.
Various generalisations have been studied in more recent years,
with a particular focus on the existence of derangements with
special properties. Written for academic researchers and
postgraduate students working in related areas of algebra, this
introduction to the finite classical groups features a
comprehensive account of the conjugacy and geometry of elements of
prime order. The development is tailored towards the study of
derangements in finite primitive classical groups; the basic
problem is to determine when such a group G contains a derangement
of prime order r, for each prime divisor r of the degree of G. This
involves a detailed analysis of the conjugacy classes and subgroup
structure of the finite classical groups.
A classical theorem of Jordan states that every finite transitive
permutation group contains a derangement. This existence result has
interesting and unexpected applications in many areas of
mathematics, including graph theory, number theory and topology.
Various generalisations have been studied in more recent years,
with a particular focus on the existence of derangements with
special properties. Written for academic researchers and
postgraduate students working in related areas of algebra, this
introduction to the finite classical groups features a
comprehensive account of the conjugacy and geometry of elements of
prime order. The development is tailored towards the study of
derangements in finite primitive classical groups; the basic
problem is to determine when such a group G contains a derangement
of prime order r, for each prime divisor r of the degree of G. This
involves a detailed analysis of the conjugacy classes and subgroup
structure of the finite classical groups.
