Fundamental Algorithms for Permutation Groups

This is the first-ever book on computational group theory.
It provides         extensive and up-to-date coverage of the
fundamental algorithms for            permutation groups with reference
to aspects of combinatorial group theory, soluble groups,
and p-groups where appropriate.
The book begins with a   constructive introduction to group
theory and algorithms for computing with small groups,
followed by a gradual discussion of the basic ideas of            Sims
for computing with very large permutation groups, and
concludes      with algorithms that use group homomorphisms, as
in the computation of Sylowsubgroups. No background in
group theory is assumed.
The emphasis is on the details of the data structures and
implementation which makes the         algorithms effective when
applied to realistic problems. The algorithms are developed
hand-in-hand with the theoretical and practical
justification. All algorithms are clearly described,
examples are given, exercises            reinforce understanding, and
detailed bibliographical remarks explain the   history and
context of the work.
Much of the later material on               homomorphisms, Sylow
subgroups, and soluble permutation groups is new.